Circular Motion is defined as the movement of an object rotating along a circular path. Objects in a circular motion can be performing either uniform or non-uniform circular motion. Motion of a car on a bank road, the motion of a bike, the well of death, etc. are examples of circular motion.
In this article, we will learn about circular motion and some related concepts, such as examples, equations, applications, etc.
What is Circular Motion?
When any object moves in a circular path, it is said to be in circular motion. For example, when a car moves around a circular track at some speed, when the hands of the analog clock are moving, or when you swing an object tied with a rope in a circular path. In all the examples of circular motion, you will generally encounter an object that will be moving at some speed (constant or varying) around a circular path. Generally, the objects tend to move in a straight motion when you apply some force. But for an object to move in a circular motion, there must be some force acting on the object continuously which will turn the object towards the center of the circular path so that the object changes its direction continuously and thus forms a circular motion.
Circular Motion Definition
In physics, circular motion can be defined as the motion in which an object moves when it follows a circular path. In circular motion the object generally moves around a fixed point and the distance between the object and the fixed point is generally fixed.
Circular Motion Example
There are many examples of circular motion which you have already encountered in your life.
Example 1: When you watch the hands of the analog clock moving in a clockwise direction, you will find that the hands are already moving in circular motion. Although it might look like the hands are actually rotating but when you will trace the motion of the tip of the hands, you will find that they are in circular motion. (We will further discuss the difference between rotational motion and circular motion in this article.)
Example 2: When you tie a stone with a rope and swung it in a circular motion (Kindly check your environment before doing this experiment as this may hurt someone).
Example 3: You must have heard that the electrons orbits in a circular path around a fixed nucleus in Bohr's Atomic model. This also constitutes the example of circular motion as the electrons are going along a circular path (in Bohr's Atomic model).
Circular Motion in Real Life
There are also situations where you have encountered circular motion of an object in real life too.
Example 1: When we go to some fair (carnival) and we want to ride the Ferris wheel. The pods of the Ferris wheel moves in a circular motion.
Example 2: A car turning on a circular track is also an example of circular motion. Generally these curves are made at an angle known as banked road which helps to reduce the role of friction to the circular motion of the car (Don't worry if you are not able to visualize this contribution of friction, we will help you visualize this later in this article).
Example 3: In your home when your mother bakes the cake, she used to make the batter for the cake first. For making the batter for the cake she stirs the spoon in a circular motion, where the mixing spoon is follows a circular path equidistant from a central point.
These real life examples helps us visualize the circular motion and we tend to conceptualize the concepts even better.
There are various new terms which comes into the picture when we talk about circular motion. These new terms generally arises from the fact that in circular motion there is angle involved so the terms, such as, angular displacement, angular velocity, or angular acceleration. The image added below shows the Angular Velocity and others in an object performing circular motion.
Let's see these concepts one by one.
Angular Displacement
Angular displacement can be defined as the measurement of the amount of rotation an object has gone through in a circular path. In circular motion, the object moves in a circular path, and angular displacement helps us observe the position of the object in a circular path. It can also be understood as the angle made by the position vector of the object between its final and initial position in the circular path.
Angular displacement is a vector quantity. The SI unit of the angular displacement is radians. It is conventionally denoted as θ. The mathematical representation of angular displacement is,
Angular Displacement(θ) = Arc Length/Radius
Therefore,
θ = S/R
where,
- S is Linear Displacement Done by Object on Circular Path
- R is Distance of Object from a Fixed Central Point (Called Radius)
Angular Velocity
Angular velocity can be defined as the rate of change of angular displacement. It is analogous to the linear velocity as it is the rate of change of linear displacement. Angular velocity can also be understood as the rate at which an object moves in a circular path.
- Angular velocity is a vector quantity. It is denoted by ω.
- SI unit of angular velocity is radian per second (rad s-1).
Mathematically, angular velocity can be represented as,
Angular Velocity (ω) = dθ/dt
We know from above that, θ = S/R
Using Angular Displacement in above equation,
ω = d/dt.(S/R)
which gives,
ω = 1/R.(dS/dt)
Finally,
ω = v/R
where,
- V is Linear Velocity and V = dS/dt
- R is Distance of Object from a Fixed Central Point
Angular Acceleration
Angular acceleration can be defined as the rate of change of angular velocity. It can be understood as the measurement of how fast or slow the angular velocity of an object is changing on the circular path. When any object starts from rest and acquires motion in circular path, it is said to have angular acceleration working on it. For example, when the Ferris wheel starts from the rest and acquires the speed, then the pods of the Ferris wheel gains angular acceleration. When the angular velocity increases, then the angular acceleration is positive. But when the angular velocity decreases, the angular acceleration is negative, i.e., angular deceleration.
- Angular acceleration is vector quantity. It is denoted by α.
- SI unit of angular acceleration is radian per second squared (rad s-2).
Angular acceleration can be represented as,
Angular acceleration (α) = dω/dt
We can substitute ω = v/R in above equation to get,
α = d/dt (v/R)
α = 1/R (dv/dt) = 1/R.(a)
Since, rate of change of linear velocity is called linear acceleration, therefore, above equation can be written as,
α = a/R
where,
- a is Linear Acceleration of Object
- R is Distance of Object from a Fixed Central Point
Equations for Circular Motion
Acceleration which an object faces in circular motion generally has two components:-
- Tangential Acceleration (aT)
- Radial Acceleration (aR)
When the object moves in a circular path, it experiences two different acceleration which works for two different purposes. One acceleration provides the magnitude of acceleration to the object while the other one is responsible for its direction. The acceleration which is responsible for the magnitude is called as tangential acceleration or linear acceleration. The acceleration which is responsible for the direction of the object moving in a circular path is called radial acceleration or centripetal acceleration. Both the tangential and the centripetal acceleration are perpendicular to each other.
Centripetal acceleration acts towards the centre of the circle and keeps the object in a circular path. This centripetal acceleration is further responsible for the Centripetal force. The normal reaction of this force is Centrifugal force which is equal in magnitude and opposite in direction to the centripetal force.
As we know the centripetal acceleration is given as, ac = V2/R. Since this acceleration is responsible for the centripetal force , therefore the centripetal force is given by,
F = mac = mV2/R
We also know from above that ω = V/R
Putting the value of V from above in centripetal force, we get,
F = mRω2
Since the object is moving in a circular path, the object must have taken some time to complete one full revolution. As we know that the time taken by the object to complete one full revolution is defined as its time period. It is denoted by T. A similar but slight different concept is frequency, which is the number of revolution made by the object in one second. Frequency is denoted by ν.
ν = 1/T
In a complete revolution, the object will move a distance of S = 2πR. Therefore, we will have V = 2πR/T
In terms of frequency we can write V = 2πRν. The angular velocity can be written as, ω=2πν. The centripetal acceleration can be written as, ac = 4π2ν2R
Centripetal Force
Centripetal force is the force which causes any object to undergo in the circular motion. This force is actually responsible for the motion of the object in the circular path.
- Centripetal force acts inward towards the center of the circular path. If the centripetal force would be absent, the object will continue to move in the straight path. For example, when we swing a ball tied to string, the ball will start moving in the circular motion.
- Centripetal force will be acting (along the string) on the ball will keep the ball in the circular path. The moment you will release the string, the ball will loose its centripetal component and then it will follow a straight path.
- Centripetal force FC is given by, FC = mV2/R, where m is the mass of the object having linear velocity V and moving along a circular path of radius R. When the time period of the object to complete one revolution is T, then the linear velocity V is given by, V = 2πR/T.
Centripetal force in terms of time period T is given by, FC = 4mπ2R/T2.
Centrifugal Force
Now lets talk about Centrifugal force. Have you been in a car when it is moving on a curve or circular path. You must have feel an outward sensation when the car moves in circular motion. While the car is moving in the circular path due to the centripetal force, what you were experiencing was actually the centrifugal force.
Centrifugal force is actually a pseudo force (not a real force) which is experienced by the object when it is moving in a circular motion. It acts in the outward direction of the circular motion.
Centrifugal force is observed in the non-inertial frame of reference. The magnitude of the centrifugal force is equal and opposite in direction to the centripetal force. That's why it is considered as the normal reaction of the the centripetal force.
Centrifugal force in terms of terms of linear velocity is given by,
FC = mV2/R
where,
- m is Mass of Object
- R is Radius of Circular Path
- V is Linear Velocity of Object Moving in Circular Motion
Applications of Centripetal Force and Centrifugal Force
Applications of centripetal force and centrifugal force are observed in our daily lives are,
Centripetal Force
- Car Turnings: When the car turns on a curved circular path, the frictional force between the road and the tyre of the car provides sufficient centripetal force to keep the car in the circular path.
- Satellites Orbiting the Planet: Gravitational pull of the planet helps providing the centripetal force which is required by the satellite to keep orbiting in a circular stable path.
- Particle Accelerator: Due to the magnetic field, the charged particles experiences the centripetal force which keeps them in the circular path.
- Amusement Ride: Rotation of the amusement ride such as merry-go-round provides the necessary centripetal force which keeps the rides in circular motion.
- Washing Machine Spin Cycle: The clothes in the washing machine are cleaned using the centripetal force which is provided by the rotating drum inside the washing machine.
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Centripetal Force ExamplesCentrifugal Force
- Car Turning: When the car turns on a circular path, the passengers sitting inside the car feels an outward push which is known as centrifugal force experienced by the passengers.
- Artificial Gravity Simulator: Artificial gravity simulator rotates simulating an artificial gravity like situation for the rider due to the centrifugal force experience by the rider in the outward direction.
- Cloth Dryers: Rotating motion of the dryer forces the cloth to move in circular motion providing centrifugal force to the wet clothes, and forcing the water droplets to move outward from the wet clothes and thus helping the clothes to dry.
- Child on a Merry-Go-Round Ride: Child experiences the outward force in a merry-go-round ride, which acts due to the centrifugal force acting on the child due to rotating motion of the ride.
- Equatorial Bulge of Earth: You may heard that the Earth is bulged at the equator and flattened at the poles. This is due to the centrifugal force acting on the Earth due its rotation which creates an outward force at the equator.
Types of Circular Motion
Circular motion can be classified into various types based on various factors. In context of physics and mechanics the object can be in circular motion in many different situations. Some common types includes:-
- Uniform Circular Motion
- Non-Uniform Circular Motion
- Planetary Motion
- Rotational Motion
But here we will learn only about, two types of circular motion, i.e., uniform circular motion and non-uniform circular motion.
When any object moves in a circular path at some constant speed then we say that the object is in uniform circular motion. Their is no change in the speed of the object and hence there is no acceleration produced. However, it is to be noted that the object is moving in a circular direction and the direction of the object is changing at every point of the path. Hence the centripetal acceleration is applying on the object at every point. This acceleration is inward in direction. But the tangential or linear acceleration is zero as the linear velocity is same.
Let's look at some examples now.
Uniform Circular Motion Examples
Uniform circular motion has many examples which can be seen around us in everyday life. In these examples the speed is constant which results in stable angular velocity. Such examples are discussed below:
- Motion of Planets: The planets are revolving around the Sun shows nearly uniform motion. Although the orbital motion are slightly elliptical in nature, they can be considered to be a circular motion.
- Ceiling Fan Blades: The blades of the ceiling fan when in full speed shows uniform circular motion, where the blades are moving at a constant speed in the circular path.
- Clock Hands: The hands of the clock moves at a contact speed in a particular circular direction. All the three different hands of the clock, i.e., the second hand, the minute hand, and the hour hand moves at constant speed, respectively.
- Ferris Ball: The pods of the Ferris wheel when moving at a constant speed, shows a uniform circular motion.
- Merry-Go-Round: The merry-go-round is a classic example of uniform circular motion. When the ride starts moving at a constant speed, the carts or the horses of the merry-go-round displays uniform circular motion as it moves along with the circular platform on which it is mounted.
Acceleration in Uniform Circular Motion
Centripetal Acceleration can be written in terms of linear velocity of the object and the radius of the circular path, and is given by,
ac = V2/R
where,
- ac is Centripetal Acceleration
- V is Magnitude of Linear Velocity of Object
- R is Radius of Circular Path
Centripetal acceleration is inversely proportional to the radius of the circular path, which means as the radius of the path decreases the centripetal acceleration increases and vice versa.
When the object moves in the circular path along a fixed central point at changing speed, more specifically when the magnitude of the velocity changes over a particular period of time, then the object is said to be in non-uniform circular motion. The change in velocity can have implication on radius in non-uniform circular motion as change in velocity can bring the change in the radius of the system of the circular path on which the object is moving.
Let's look at some examples now.
Examples of Non-Uniform Circular Motion
Examples of non-uniform circular motion shows change in speed, and angular velocity which results in varied motion of the object along the circular path. These examples show changing velocity over time, either increasing or decreasing. Such examples include,
- Roller Coster: Suppose a roller coster makes a loop like ride which is circular in motion. Then the roller coster will approach the loop with a particular speed and then in the middle of the loop the speed will decrease but as soon as the coster will approach the end of the loop its speed will increase. Thus showing varying speed profile and therefore, can be an example of non-uniform circular motion.
- Car on curved road: In practical life, the car making a turn at a curved road usually lower its speed and thus resulting in change in speed further resulting in negative acceleration, i.e., deceleration. This is also an example of non-uniform circular motion.
- Amusement Ride: Small Ferris wheel in amusement park or fair is usually moved with the help of a human, which moves the Ferris wheel at varying speed. Thus the speed of the pods of the Ferris wheel experiences non-uniform circular motion.
Acceleration in Non-Uniform Circular Motion
In non-uniform circular motion, as the speed or the angular velocity of the object changes, it experiences both the acceleration. Therefore, the acceleration in non-uniform circular motion has two components, i.e., the tangential acceleration as well as the centripetal acceleration.
- Tangential Acceleration: This component of acceleration acts along the tangent to the circular path. Tangential acceleration generally changes the magnitude of the linear velocity. Tangential acceleration is given by,
at = dV/dt
where
- at is Tangential Acceleration
- dV is Change in Velocity
- dT is Change in Time
- Centripetal Acceleration: This component of acceleration acts towards the centre of the circular path. It is directed inward towards the centre of the circular path. It is also called the radial acceleration. Centripetal acceleration is given by,
ac = V2/R
where
- at is Centripetal Acceleration
- V is Velocity
- R is Radius of Circular Path
Application of Circular Motion
Application of circular motion can be found in our everyday life as well as in practical situations. Various application includes,
Turning of Vehicles at Banked Road
As we know that the centripetal force which is directed towards the centre of a vehicle moving at a circular road is given by, FC = mV2/R. This force is provided by the force of friction which is between the tyre of the vehicle and the surface of the road.
Note that it is the static friction which provides the centripetal force. Suppose the static frictional coefficient is μS and R is the radius of the circular road. Then the maximum speed at which the vehicle can drive at the circular flat road is given by,
Vmax = √(μSRg)
As the velocity of the vehicle is dependent on the μs and R, and the radius is generally not changeable. We can reduce the contribution of the static friction on the vehicle in a circular motion if we can make the road banked at an angle.
Let the angle at which the road is banked be θ.
As the vertical component has no acceleration part, its net force must be zero, therefore,
N cosθ = mg + Fsinθ
Horizontal component is solely responsible for the centripetal force acting on the vehicle, therefore,
Nsinθ + Fcosθ = mv2/R
Since F is less than μsN. Therefore, in order to have the maximum velocity, we have to put,
FS = μsN
Therefore, the equation of the vertical components will become,
N cosθ = mg + μsNsinθ
And Horizontal component will become,
Nsinθ + μsNcosθ = mv2/R
From vertical component, we can get the value of N to be,
N = \frac{mg}{cos\theta-\mu_ssin\theta}
Putting this value of N in horizontal component, we get,
\frac{mg(sin\theta+\mu_scos\theta)}{cos\theta-\mu_ssin\theta} = \frac{mV_{max}^2}{R}
Rearranging the term and dividing the left hand side of the equation with cosθ, we get Vmax to be,
V_{max} = \sqrt{\frac{Rg(\mu_s+tan\theta)}{1-\mu_stan\theta}}
Comparing this maximum speed with the maximum speed of the vehicle at the flat road, we can clearly see that this term has some other part in the equation which increases the maximum speed with which the vehicle can move at a banked road in a circular motion.
Below is listed a table to differentiate between uniform circular motion and non-uniform circular motion.
Uniform Circular Motion Vs Non-Uniform Circular Motion |
|---|
Characteristics | Uniform Circular Motion | Non-uniform Circular Motion |
|---|
Linear Velocity | Constant magnitude | Varying magnitude (increase or decrease) |
|---|
Angular Velocity | Constant over time | Can increase, decrease or remain constant over time |
|---|
Angular Acceleration | Remains Zero as there is no change in angular velocity | Can have varying value as there is change in angular velocity |
|---|
Centripetal Acceleration | Constant magnitude | Magnitude can change (increase or decrease) |
|---|
Tangential Acceleration | Zero as the linear velocity is not changing | Non-zero as there is change in linear velocity over time. |
|---|
Time Period | Constant | Can be constant or changing |
|---|
Frequency | Constant | Can be constant or changing |
|---|
Example | Motion of Planets around Sun in the orbit | Car turning on the circular path with varying speed |
|---|
Circular Motion and Rotational Motion
Below table highlights the difference between the circular motion and the rotational motion.
Difference Between Circular Motion and Rotational Motion |
|---|
Characteristics | Circular Motion | Rotational Motion |
|---|
Definition | Motion of object when it moves in circular path | Motion of object when it rotates around an axis |
|---|
Defined Path of movement | Circular as the object moves along the circular path | Circular but the object rotates along a fixed axis of rotation |
|---|
Axis of Rotation | Outside the body | Inside the body |
|---|
Reference Point | Centre of the circular path | Axis of the rotation |
|---|
Angular Displacement | Angle through which the object has moved along the circular path | Angle through which the object has rotated along the axis of rotation |
|---|
Angular Velocity | Rate of change of angular displacement with respect to time | Rate of change of rotational speed with respect to time |
|---|
Angular Acceleration | Rate of change of angular velocity with respect to time | Rate of change of rotational speed with respect to time |
|---|
Example | Earth revolving around the Sun in an orbit causing seasonal changes | Earth rotating on its own axis of rotation in the orbit causing day and night |
|---|
Circular Motion formulas are added in the table below,
Physical Quantity | Denoted by | Formula |
|---|
Angular Displacement | θ | θ = S/R |
|---|
Angular Velocity | ω | ω = V/R |
|---|
Angular Acceleration (Tangential) | α | α = a/R |
|---|
Centripetal Acceleration | ac | ac = V2/R |
|---|
Centripetal Force (in terms of V) | Fc | Fc = mV2/R |
|---|
Centripetal Force (in terms of ω) | Fc | Fc = mRω2 |
|---|
Frequency (in terms of Time period) | ν | ν = 1/T |
|---|
Linear velocity (in terms of Frequency) | V | V = 2πRν |
|---|
Angular velocity (in terms of Frequency) | ω | ω = 2πν |
|---|
Centripetal Acceleration (in terms of ν) | ac | ac = 4π2ν2R |
|---|
Learn More,
Circular Motion - Solved Examples
Example 1: Find the angular velocity of the boy who is riding the bicycle at a speed of 10 ms-1 on a circular path of radius 25 m.
Solution:
We have given,
- Linear speed of the boy as he is riding the bicycle, V = 10 ms-1
- Radius of the circular path, R = 25 m
We know that, the angular velocity of the boy riding the bicycle on a circular path can be obtained by using the given formula,
\omega = \frac{V}{R}
Substituting the value of V and R in the formula of angular velocity, we get,
\omega = \frac{10\,ms^{-1}}{25\,m}
\omega = 0.4\,rad\,s^{-1}
Therefore, the angular velocity (ω) of the boy who is riding the bicycle at a speed of 10 ms-1 on a circular path of radius 25 m is 0.4 rad s-1 .
Example 2: In the above problem, if the mass of the boy is 35 kg then calculate the centripetal acceleration of the boy and also find the centrifugal force acting on the boy.
Solution:
We know that centripetal acceleration is given by,
a_c = \frac{V^2}{R}
Substituting the value of V and R in above formula, we get,
a_c = \frac{{(10\,ms^{-1})}^2}{25\,m}
ac = 4 ms-2
Now, the centrifugal force can be given by the,
F_c = \frac{mV^2}{R}
As the mass of the boy is given to be m = 35 kg, therefore,
F_c = \frac{35\,kg.{(10ms^{-1})}^2}{25\,m}
Fc = 140 N
Therefore, centripetal acceleration of the boy is 4 ms-2 and the centrifugal force experienced by the boy is 140 N.
Example 3: Suppose a motorcyclist is making a turn at a speed of 10 ms-2. How will the force acting towards the centre will change if he doubles its speed?
Solution:
As we know, the centripetal force is given by,
F_c = \frac{mV^2}{R}
Since, the centripetal force is directly proportional to the square of the speed, i.e.,
F_c \propto V^2
Therefore, when the speed will get doubles, the centripetal force acting on the motorcyclist will increase to 4 times.
Example 4: A car is going in a non-uniform motion on curve of circular path, and its tangential acceleration is given as 3 ms-2, while its centripetal acceleration is given as 4 ms-2. Calculate its total acceleration.
Solution:
Given,
- Tangential Acceleration (at) = 3 ms-2
- Centripetal Acceleration (ac) = 4 ms-2
We know that the total acceleration is given by,
a = \sqrt{a_t^2\,+\,a_c^2}
Substituting values, we get,
a = \sqrt{{(3\,ms^{-2})}^2\,+\,{(4\,ms^{-2})}^2}
a = \sqrt{9\,+\,16} = \sqrt{25} = 5\,ms^{-2}
Therefore the total acceleration is 5 ms-2.
Example 5: An insect is trapped in a circular groove of radius 10 cm moves along the groove steadily and completes 5 revolutions in 100 seconds. What is the angular speed and linear speed of the motion?
Solution:
Given,
- Radius, R = 10 cm
- Total revolution made = 2\pi \times5
- Time taken, T = 100 s
Therefore angular speed, ω is given by,
\omega = \frac{Total\,revolution\,made}{Time\,taken}
\omega = \frac{2\pi\times5}{100\,s}
\omega = 0.31\,rad\,s^{-1}
The linear speed, V is given by,
V = ωR
V = 0.31\,s^{-1}\,\times\,10\,cm = 3.1\,cm\,s^{-1}
Therefore, the angular speed is 0.31\,rad\,s^{-1}
and the linear speed is 3.1\,cm\,s^{-1}
.
Circular Motion - Numericals
Q1: A boy with a mass of 25 kg is rides his cycle in a circular path at a speed of 2.5 ms-1. If the radius of the circular path is 2.5 m, then calculate the centripetal acceleration of the boy.
Q2: A boy is riding a merry-go-round. If he completes 10 revolutions in 20 seconds. Calculate its angular velocity.
Q3: A car of mass 500 kg is moving on a circular path of radius 150 m. The car is moving at a constant speed of 50 ms-1. How much force is required to keep the car in circular motion?
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Speed and VelocityMechanics can be termed as the branch of physics concerned with the concepts of energy and forces and their effect on bodies. It governs the relationships related to the motion of objects, that is, between matter, force, and its associated energy. It is responsible for the motion of bodies and the a
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AccelerationAcceleration is defined as the rate of change in velocity. This implies that if an object’s velocity is increasing or decreasing, then the object is accelerating. Acceleration has both magnitude and direction, therefore it is a Vector quantity. According to Newton's Second Law of Motion, acceleratio
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What is Momentum Equation?What is Momentum in Physics?The concept of Momentum in physics is very important, without which most of the theories in physics will fail. The momentum can be calculated by multiplying the mass of the substance and its velocity. In physics, momentum is of different types and forms. Let's know more a
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Equations of Motion: Derivations and ExamplesEquations of Motion was given by Sir Issac Newton; who is considered the father of mechanics. He was the first to give the fundamental physical laws that deal with objects and their motion. He formulated three equations of motion of an object and published them in his book Philosophiae Naturalis Pri
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Uniform Circular MotionUniform Circular Motion as the name suggests, is the motion of a moving object with constant speed in a circular path. As we know, motion in a plane only has two coordinates, either x, and y, y and z, or z and x. Except for Projectile motion, circular motion is also an example of motion in a 2-D pla
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Projectile MotionProjectile motion refers to the curved path an object follows when it is thrown or projected into the air and moves under the influence of gravity. In this motion, the object experiences two independent motions: horizontal motion (along the x-axis) and vertical motion (along the y-axis). Projectile
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Relative MotionRelative motion explains how the movement of an object is perceived differently depending on the observer’s frame of reference. For instance, while sitting on a moving train, a stationary train on the track appears to move backwards. This happens because the motion of the train you are in influences
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Rotational Mechanics
Concepts of Rotational MotionRotational motion refers to the movement of an object around a fixed axis. It is a complex concept that requires an understanding of several related concepts. Some of the important concepts related to rotational motion include angular displacement, angular velocity, angular acceleration, torque, the
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Angular MotionAngular Motion is the motion of an object around a fixed axis or point, or along a curved path with a constant angular velocity. It is also known as rotational motion. Another motion of an object is termed linear motion, which is a motion along a straight route. Linear motion variables are measured
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Angular FrequencyAngular frequency is a fundamental concept in physics, particularly in studying wave motion and oscillations. It measures the angular displacement of a particle per unit time. In this article, we will learn about the meaning and definition of angular frequency, the formula of angular frequency, the
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Rotational Kinetic EnergyRotational Kinetic Energy is described as the kinetic energy associated with the rotation of an object around an axis. It is also known as angular kinetic energy. It is dependent on the mass of an object and its angular velocity. In this article, we will learn about rotational kinetic energy, its fo
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TorqueTorque is the effect of force when it is applied to an object containing a pivot point or the axis of rotation (the point at which an object rotates), which results in the form of rotational motion of the object. The Force causes objects to accelerate in the linear direction in which the force is ap
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Angular MomentumAngular Momentum is a kinematic characteristic of a system with one or more point masses. Angular momentum is sometimes called Rotational Momentum or Moment of Momentum, which is the rotational equivalent of linear momentum. It is an important physical quantity as it is conserved for a closed system
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Centre of MassCentre of Mass is the point of anybody where all the mass of the body is concentrated. For the sake of convenience in Newtonian Physics, we take the body as the point object where all its mass is concentrated at the centre of mass of the body. The centre of mass of the body is a point that can be on
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Centre of GravityCentre of Gravity is one of the fundamental concepts in the study of gravitational force. Engineers and Scientists while dealing with mechanics and gravity often come across solid bodies which can't be represented by point masses such as celestial objects. In those cases, it is assumed as well as pr
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Radius of GyrationRadius of gyration, R, is a measure used in mechanics and engineering to describe the distribution of mass or inertia of an object relative to its axis of rotation. Radius of Gyration, or the radius of a body, is always centered on its rotational axis. It is a geometric characteristic of a rigid bod
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Moment of InertiaMoment of Inertia is a property of a body in rotational motion that resists changes in its rotational state. It is analogous to mass (inertia) in linear motion. Mathematically, it is defined as the sum of the product of each particle’s mass and the square of its distance from the axis of rotation: I
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Fluid Mechanics
Mechanical Properties of FluidsFluids are substances that can flow and adapt to the shape of their container, including liquids and gases like water and air. Mechanical properties of fluids refer to viscosity, density, and pressure, which describe how fluids respond to external forces and influence their behavior in various situa
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What is Viscosity?Viscosity is a fundamental property of liquids that describes their internal resistance to flow. Imagine three bowls—one filled with water and the other with oil and honey. If you were to tip the three bowls and observe the flow, you’d quickly notice that water pours out much faster than oil and hon
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Buoyant ForceBuoyancy is a phenomenon due to the buoyant force that causes an object to float. When you put an object in a liquid, an upward force is exerted on the object by the liquid. This force is equal to the weight of the liquid that has been displaced. The amount of liquid that has been displaced depends
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Archimedes PrincipleArchimedes Principle is a fundamental concept in fluid mechanics, credited to the ancient Greek mathematician and physicist Archimedes. According to Archimedes' Principle, when an object is immersed in a fluid the object experiences an upward force whose magnitude is equal to the weight of the fluid
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Pascal's LawPascal's law establishes the relation between pressure and the height of static fluids. A static fluid is defined as a fluid that is not in motion. When the fluid is not flowing, it is said to be in hydrostatic equilibrium. For a fluid to be in hydrostatic equilibrium, the net force on the fluid mus
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Reynolds NumberAs liquid runs into a channel, it collides with the pipe. Engineers ensure that the liquid flow through the city's pipes is as consistent as possible. As a result, a number known as the Reynolds number predicts whether the flow of the liquid will be smooth or turbulent. Sir George Stoke was the firs
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Streamline FlowThe substance that can change its form under an external force is defined as fluid. Whenever an external force is applied to a fluid, it begins to flow. The study of fluids in motion is defined as fluid dynamics. Have you ever noticed a creek flowing beneath the bridge? When you see a streamline, wh
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Laminar and Turbulent FlowLaminar flow and turbulent flow describe the movement patterns of fluids. Laminar flow is characterized by smooth, orderly layers of fluid sliding over one another without mixing, ideal for scenarios where minimal resistance is desired. Turbulent flow features chaotic, swirling patterns with irregul
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Bernoulli's PrincipleBernoulli's Principle, formulated by Daniel Bernoulli and later expressed as Bernoulli's Equation by Leonhard Euler in 1752, is a fundamental concept in fluid mechanics. It describes the relationship between the pressure (P), velocity, and height (h) of a fluid in motion. The principle states that i
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Poiseuilles Law FormulaAccording to Poiseuille's law, the flow of liquid varies depending on the length of the tube, the radius of the tube, the pressure gradient and the viscosity of the fluid. It is a physical law that calculates the pressure drop in an incompressible Newtonian fluid flowing in laminar flow through a lo
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Stoke's LawStoke's Law: Observe a raindrop falling from a height if you look closely you will notice that the speed of all the raindrops is constant and even though it falls from a height under the influence of gravity its velocity seems constant. These questions are answered using Stoke's lawStoke's law was f
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Solid Mechanics
What is Stress?Stress in physics is defined as the force exerted on the unit area of a substance. Stress affects the body as strain in which the shape of the body changes if the stress is applied and sometimes it gets permanently deformed. On the basis of the direction of force applied to the body, we can categori
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Stress and StrainStress and Strain are the two terms in Physics that describe the forces causing the deformation of objects. Deformation is known as the change of the shape of an object by applications of force. The object experiences it due to external forces; for example, the forces might be like squeezing, squash
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Stress-Strain CurveStress-Strain Curve is a very crucial concept in the study of material science and engineering. It describes the relationship between stress and the strain applied on an object. We know that stress is the applied force on the material, and strain, is the resulting change (deformation or elongation)
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Elasticity and PlasticityYou've undoubtedly heard of the idea of elasticity by now. In layman's words, it indicates that after being stretched, some substances return to their former form. You've experimented with a slingshot. Didn't you? That is an elastic substance. Let us go into the ideas of elasticity and plasticity to
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Modulus of ElasticityModulus of Elasticity or Elastic Modulus is the measurement of resistance offered by a material against the deformation force acting on it. Modulus of Elasticity is also called Young's Modulus. It is given as the ratio of Stress to Strain. The unit of elastic modulus is megapascal or gigapascal Modu
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Modulus of RigidityModulus of rigidity also known as shear modulus, is used to measure the rigidity of a given body. It is the ratio of shear stress to shear strain and is denoted by G or sometimes by S or μ. The modulus of rigidity of a material is directly proportional to its elastic modulus which depends on the mat
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Young's ModulusYoung's Modulus is the ratio of stress and strain. It is named after the famous British physicist Thomas Young. It is also known as the "Modulus of Elasticity" and is a fundamental property that describes the relationship between stress and strain in elastic materials. It explains how a material def
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Bulk Modulus FormulaThe modulus of elasticity measures a material's resistance to elastic deformation under external forces. Understanding this property is important for designing structures with materials like metals, concrete, and polymers to ensure they can withstand stresses without permanent deformation.The modulu
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Shear Modulus and Bulk ModulusA rigid body model is an idealised representation of an item that does not deform when subjected to external forces. It is extremely beneficial for evaluating mechanical systems—and many physical items are quite stiff. The degree to which an item may be regarded as stiff is determined by the physica
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Poisson's RatioPoisson's Ratio is the negative ratio of transversal strain or lateral strain to the longitudinal strain of a material under stress. When a material particularly a rubber-like material undergoes stress the deformation is not limited to only one direction, rather it happens along both transversal and
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Stress, Strain and Elastic Potential EnergyElasticity, this term always reminds of objects like Rubber bands, etc. However, if the question arises, which one is more elastic- A rubber or an Iron piece? The answer will be an Iron piece. Why? The answer lies in the definition of Elasticity, elasticity is known to be the ability of the object t
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Thermodynamics
Basics Concepts of ThermodynamicsThermodynamics is concerned with the ideas of heat and temperature, as well as the exchange of heat and other forms of energy. The branch of science that is known as thermodynamics is related to the study of various kinds of energy and its interconversion. The behaviour of these quantities is govern
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Zeroth Law of ThermodynamicsZeroth Law of Thermodynamics states that when two bodies are in thermal equilibrium with another third body than the two bodies are also in thermal equilibrium with each other. Ralph H. Fowler developed this law in the 1930s, many years after the first, second, and third laws of thermodynamics had a
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First Law of ThermodynamicsFirst Law of Thermodynamics adaptation of the Law of Conservation of Energy differentiates between three types of energy transfer: Heat, Thermodynamic Work, and Energy associated with matter transfer. It also relates each type of energy transfer to a property of a body's Internal Energy. The First L
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Second Law of ThermodynamicsSecond Law of Thermodynamics defines that heat cannot move from a reservoir of lower temperature to a reservoir of higher temperature in a cyclic process. The second law of thermodynamics deals with transferring heat naturally from a hotter body to a colder body. Second Law of Thermodynamics is one
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Thermodynamic CyclesThermodynamic cycles are used to explain how heat engines, which convert heat into work, operate. A thermodynamic cycle is used to accomplish this. The application determines the kind of cycle that is employed in the engine. The thermodynamic cycle consists of a series of interrelated thermodynamic
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Thermodynamic State Variables and Equation of StateThe branch of thermodynamics deals with the process of heat exchange by the gas or the temperature of the system of the gas. This branch also deals with the flow of heat from one part of the system to another part of the system. For systems that are present in the real world, there are some paramete
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Enthalpy: Definition, Formula and ReactionsEnthalpy is the measurement of heat or energy in the thermodynamic system. It is the most fundamental concept in the branch of thermodynamics. It is denoted by the symbol H. In other words, we can say, Enthalpy is the total heat of the system. Let's know more about Enthalpy in detail below.Enthalpy
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State FunctionsState Functions are the functions that are independent of the path of the function i.e. they are concerned about the final state and not how the state is achieved. State Functions are most used in thermodynamics. In this article, we will learn the definition of state function, what are the state fun
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Carnot EngineA Carnot motor is a hypothetical motor that works on the Carnot cycle. Nicolas Leonard Sadi Carnot fostered the fundamental model for this motor in 1824. In this unmistakable article, you will find out about the Carnot cycle and Carnot Theorem exhaustively. The Carnot motor is a hypothetical thermod
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Heat Engine - Definition, Working, PV Diagram, Efficiency, TypesHeat engines are devices that turn heat energy into motion or mechanical work. Heat engines are based on the principles of thermodynamics, specifically the conversion of heat into work according to the first and second laws of thermodynamics. They are found everywhere, from our cars, power plants to
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Wave and Oscillation
Introduction to Waves - Definition, Types, PropertiesA wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities in physics, mathematics, and related subjects, commonly described by a wave equation. At least two field quantities in the wave medium are involved in physical waves. Periodic waves occur when variables o
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Wave MotionWave Motion refers to the transfer of energy and momentum from one point to another in a medium without actually transporting matter between the two points. Wave motion is a kind of disturbance from place to place. Wave can travel in solid medium, liquid medium, gas medium, and in a vacuum. Sound wa
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OscillationOscillations are defined as the process of repeating vibrations of any quantity about its equilibrium position. The word “oscillation†originates from the Latin verb, which means to swing. An object oscillates whenever a force pushes or pulls it back toward its central point after displacement. This
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Oscillatory Motion FormulaOscillatory Motion is a form of motion in which an item travels over a spot repeatedly. The optimum situation can be attained in a total vacuum since there will be no air to halt the item in oscillatory motion friction. Let's look at a pendulum as shown below. The vibrating of strings and the moveme
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Amplitude FormulaThe largest deviation of a variable from its mean value is referred to as amplitude. It is the largest displacement from a particle's mean location in to and fro motion around a mean position. Periodic pressure variations, periodic current or voltage variations, periodic variations in electric or ma
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What is Frequency?Frequency is the rate at which the repetitive event that occurs over a specific period. Frequency shows the oscillations of waves, operation of electrical circuits and the recognition of sound. The frequency is the basic concept for different fields from physics and engineering to music and many mor
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Amplitude, Time Period and Frequency of a VibrationSound is a form of energy generated by vibrating bodies. Its spread necessitates the use of a medium. As a result, sound cannot travel in a vacuum because there is no material to transfer sound waves. Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is
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Energy of a Wave FormulaWave energy, often referred to as the energy carried by waves, encompasses both the kinetic energy of their motion and the potential energy stored within their amplitude or frequency. This energy is not only essential for natural processes like ocean currents and seismic waves but also holds signifi
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Simple Harmonic MotionSimple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the memb
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Displacement in Simple Harmonic MotionThe Oscillatory Motion has a big part to play in the world of Physics. Oscillatory motions are said to be harmonic if the displacement of the oscillatory body can be expressed as a function of sine or cosine of an angle depending upon time. In Harmonic Oscillations, the limits of oscillations on eit
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Sound
Production and Propagation of SoundHave you ever wonder how are we able to hear different sounds produced around us. How are these sounds produced? Or how a single instrument can produce a wide variety of sounds? Also, why do astronauts communicate in sign languages in outer space? A sound is a form of energy that helps in hearing to
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What are the Characteristics of Sound Waves?Sound is nothing but the vibrations (a form of energy) that propagates in the form of waves through a certain medium. Different types of medium affect the properties of the wave differently. Does this mean that Sound will not travel if the medium does not exist? Correct. It will not, It is impossibl
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Speed of SoundSpeed of Sound as the name suggests is the speed of the sound in any medium. We know that sound is a form of energy that is caused due to the vibration of the particles and sound travels in the form of waves. A wave is a vibratory disturbance that transfers energy from one point to another point wit
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Reflection of SoundReflection of Sound is the phenomenon of striking of sound with a barrier and bouncing back in the same medium. It is the most common phenomenon observed by us in our daily life. Let's take an example, suppose we are sitting in an empty hall and talking to a person we hear an echo sound which is cre
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Refraction of SoundA sound is a vibration that travels as a mechanical wave across a medium. It can spread via a solid, a liquid, or a gas as the medium. In solids, sound travels the quickest, comparatively more slowly in liquids, and the slowest in gases. A sound wave is a pattern of disturbance caused by energy trav
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How do we hear?Sound is produced from a vibrating object or the organ in the form of vibrations which is called propagation of sound and these vibrations have to be recognized by the brain to interpret the meaning which is possible only in the presence of a multi-functioning organ that is the ear which plays a hug
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Audible and Inaudible SoundsWe hear sound whenever we talk, listen to some music, or play any musical instrument, etc. But did you ever wondered what is that sound and how is it produced? Or why do we hear to our own voice when we shout in a big empty room loudly? What are the ranges of sound that we can hear? In this article,
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Explain the Working and Application of SONARSound energy is the type of energy that allows our ears to sense something. When a body vibrates or moves in a ‘to-and-fro' motion, a sound is made. Sound needs a medium to flow through in order to propagate. This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a
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Noise PollutionNoise pollution is the pollution caused by sound which results in various problems for Humans. A sound is a form of energy that enables us to hear. We hear the sound from the frequency range of 20 to 20000 Hertz (20kHz). Humans have a fixed range for which comfortably hear a sound if we are exposed
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Doppler Effect - Definition, Formula, ExamplesDoppler Effect is an important phenomenon when it comes to waves. This phenomenon has applications in a lot of fields of science. From nature's physical process to planetary motion, this effect comes into play wherever there are waves and the objects are traveling with respect to the wave. In the re
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Doppler Shift FormulaWhen it comes to sound propagation, the Doppler Shift is the shift in pitch of a source as it travels. The frequency seems to grow as the source approaches the listener and decreases as the origin fades away from the ear. When the source is going toward the listener, its velocity is positive; when i
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Electrostatics
ElectrostaticsElectrostatics is the study of electric charges that are fixed. It includes an study of the forces that exist between charges as defined by Coulomb's Law. The following concepts are involved in electrostatics: Electric charge, electric field, and electrostatic force.Electrostatic forces are non cont
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Electric ChargeElectric Charge is the basic property of a matter that causes the matter to experience a force when placed in a electromagnetic field. It is the amount of electric energy that is used for various purposes. Electric charges are categorized into two types, that are, Positive ChargeNegative ChargePosit
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Coulomb's LawCoulomb’s Law is defined as a mathematical concept that defines the electric force between charged objects. Columb's Law states that the force between any two charged particles is directly proportional to the product of the charge but is inversely proportional to the square of the distance between t
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Electric DipoleAn electric dipole is defined as a pair of equal and opposite electric charges that are separated, by a small distance. An example of an electric dipole includes two atoms separated by small distances. The magnitude of the electric dipole is obtained by taking the product of either of the charge and
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Dipole MomentTwo small charges (equal and opposite in nature) when placed at small distances behave as a system and are called as Electric Dipole. Now, electric dipole movement is defined as the product of either charge with the distance between them. Electric dipole movement is helpful in determining the symmet
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Electrostatic PotentialElectrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit
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Electric Potential EnergyElectrical potential energy is the cumulative effect of the position and configuration of a charged object and its neighboring charges. The electric potential energy of a charged object governs its motion in the local electric field.Sometimes electrical potential energy is confused with electric pot
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Potential due to an Electric DipoleThe potential due to an electric dipole at a point in space is the electric potential energy per unit charge that a test charge would experience at that point due to the dipole. An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific
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Equipotential SurfacesWhen an external force acts to do work, moving a body from a point to another against a force like spring force or gravitational force, that work gets collected or stores as the potential energy of the body. When the external force is excluded, the body moves, gaining the kinetic energy and losing a
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Capacitor and CapacitanceCapacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications,
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