Centripetal Force Formula with Examples Last Updated : 23 Jul, 2025 Comments Improve Suggest changes Like Article Like Report Centripetal force is a force that operates on a body traveling in a circular direction and is directed toward the center around which the body is moving. When an item moves at a constant speed around a circular route, it encounters an accelerating centripetal force toward the center.Table of ContentWhat is Centripetal Force?Centripetal Force FormulaDerivation of FormulaExamples of Centripetal ForceSample Problems on Centripetal Force Centripetal Force WorksheetWhat is Centripetal Force?In the uniform circular motion of a particle, the centripetal force is the force on the particle which at every instant points radially towards the center of the circle and produces the centripetal acceleration to move the particle in its circular path.Centripetal Force FormulaFc = m × v2/rWhere,Fc is the centripetal forcem is massv is velocityr is the radius of the pathDerivation of FormulaThe force of a moving object isF = maPQ + QS = PS-v1 + v2 = ΔvΔv = v2 - v1The PQS and AOB triangles are similar. Therefore,Δv/AB = v/rAB = vΔtΔv/v×Δt = v/rΔv/Δt = v2/ra = v2/rNow, Fc = maTherefore, Fc = m × v2/rExamples of Centripetal ForceWhen a metal bob tied to one end of a string is whirled around a circle the tension in the string is centripetal force. If the hold at the Centre is released, the bob flies away tangentially.For the motion of the moon or a satellite around the earth, the gravitational force provides the centripetal force.We know that the electrons revolve around the nucleus in nearly circular orbits. The electrostatic force between the electrons and the nucleus provides the centripetal force.When a pendulum is pulled away from its equilibrium position and is pushed tangentially, it moves along a circle. The horizontal component of tension T provides the centripetal force. For an Earth-satellite in a circular orbit, the centri- petal force is the gravitational force exerted by the Earth on the satellite.In the Bohr atom, the centripetal force on an elec- tron in circular orbit around the nucleus is the attractive Coulomb force of the nucleus.When an object tied at the end of a string is revolved in a horizontal circle, the centripetal force is the tension in the string.When a car takes a turn in a circular arc on a horizontal road with constant speed, the force of static friction between the car tyres and road surface is the centripetal force.Sample Problems on Centripetal Force Problem 1: A van of 1,250 Kg is travelling at 50.0 m/s and covers a curve of the radius of 200 m. calculate the centripetal force.SolutionMass = 1,250 KgRadius = 200 mVelocity = 50.0 m/sWe know that ,Centripetal force (Fc)= mv2/r= 1250 × (50)2 / 200= 15,625 NProblem 2: A car of mass 1000 kg is moving in a circular path with a velocity of 1.8 km/h. If the radius of a circular path is 10 m, then what is the centripetal force acting on a car?SolutionMass of a car, m = 1000 kgVelocity of a car, v = 1.8 km/h = 0.5 m/sRadius of a circular path, r = 10 mUsing the equation of centripetal force,Fc = m v2 /rFc = [1000 × (0.5)2] /10Fc = 250 /10Fc = 25 NTherefore, the centripetal force acting on a car is 25 N.Problem 3: One boy of mass 30 kg is enjoying a merry-go-round ride. A boy sitting on a merry-go-round rotates in a circular path of radius 6 m with a velocity of 2 m/s. Calculate the centripetal force acting on a boy.SolutionMass of a boy, m = 30 kgRadius of a circular path, r = 6 mVelocity of a boy, v = 2 m/sUsing the equation of centripetal force,Fc = mv2 / rFc = [30 × (2)2] /6Fc = 120 /6Fc = 20 NTherefore, the centripetal force acting on a boy is 20 N.Problem 4: Calculate the centripetal force acting on a 2500 kg truck moving with a velocity of 1.2 km/h in a circular path of a radius of 15 m.SolutionMass of a truck, m = 2500 kgVelocity of a truck, v = 1.2 km/h = 0.33 m/sRadius of a circular path, r = 15 mUsing the equation of centripetal force,Fc = mv2/ rFc = [2500 × (0.33)2] /15Fc = 272.25 /15Fc = 18.15 NTherefore, the centripetal force acting on a truck is 18.15 NProblem 5: What is the centripetal force acting on a sports bike of mass 140 kg moving in a circular path of radius 25 m with a velocity of 2.5 km/h?SolutionMass of a sports bike, m = 140 kgRadius of a circular path, r = 25 mVelocity of a sports bike, v = 2.5 km/h = 0.69 m/sUsing the equation of centripetal force,Fc = mv2/rFc = [140 × (0.69)2] /25Fc = 66.654 /25Fc = 2.6 NTherefore, the centripetal force acting on a sports bike is 2.6 N.Centripetal Force WorksheetProblem 1: A car is moving in a circular path with a radius of 50 meters at a constant speed of 20 m/s. Calculate the centripetal force acting on the car if its mass is 1000 kg.Problem 2: A stone tied to a string is being whirled in a horizontal circle with a radius of 2 meters. If the stone has a mass of 0.5 kg and is moving with a speed of 5 m/s, what is the tension in the string?Problem 3: A 2 kg object is moving in a circular path of radius 3 meters at a constant speed of 4 m/s. Calculate the centripetal acceleration of the object.Problem 4: A ball of mass 0.2 kg is moving in a circular path with a radius of 0.5 meters. If the centripetal force acting on the ball is 8 N, calculate its speed.Problem 5: Define centripetal force. Explain its role in circular motion.Problem 6: A roller coaster car is moving at a speed of 10 m/s around a vertical loop with a radius of 15 meters. Calculate the centripetal force acting on a passenger of mass 70 kg at the top of the loop.Problem 7: A car is navigating a curve of radius 80 meters at a speed of 25 m/s. Calculate the minimum coefficient of friction required between the tires and the road to prevent skidding.Problem 8: A 5 kg object is attached to a string and is being whirled in a vertical circle with a radius of 2 meters. Calculate the tension in the string at the bottom of the circle if the object is moving with a speed of 6 m/s.Problem 9: A car is moving around a circular track of radius 100 meters with a constant speed of 30 m/s. Calculate the centripetal acceleration and the centripetal force acting on the car if its mass is 1500 kg.Problem 10: A particle of mass 0.4 kg is moving in a circular path with a radius of 0.6 meters at a constant angular speed of 2 rad/s. Calculate the centripetal force acting on the particle.Also Read:Centripetal Force and Centrifugal Force Difference Between Centripetal Force and Centrifugal Force Comment More infoAdvertise with us P priti0608 Follow Improve Article Tags : School Learning Physics Physics-Formulas Similar Reads Physics Tutorial The term "physics" is derived from the Greek word physis (meaning “natureâ€) and physika (meaning “natural thingsâ€). It is the study of matter, energy, and the fundamental forces of nature, seeking to understand the behaviour of the universe from the smallest subatomic particles to the largest galaxi 15+ min read MechanicsRest and MotionRest and motion describe the state of objects in relation to their surroundings. Whether an object is at rest or in motion, these states can be analyzed and understood through the principles of physics. 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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 12 min read 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 7 min read 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. 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For systems that are present in the real world, there are some paramete 5 min read 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 12 min read 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 7 min read 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. 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Sound vibration is the back and forth motion of an entity that causes the sound to be made. That is 5 min read 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 7 min read 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 15+ min read 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 10 min read SoundProduction 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 6 min read 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 7 min read 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 12 min read 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 9 min read 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. 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This medium could be in the form of a gas, a liquid, or a solid. Sound propagates through a 8 min read 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 8 min read 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 7 min read 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 3 min read ElectrostaticsElectrostaticsElectrostatics 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 13 min read 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 8 min read 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 9 min read 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 11 min read 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 6 min read 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 12 min read 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 15+ min read 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 7 min read 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 9 min read 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, 11 min read Like