Understanding Galilean Transformation: Foundation of Classical Mechanics and Motion in Inertial Frames
- 1. GALILEAN TRANSFORMATION Presented by: Abhishek Kumar M.Sc (Physics) A.N. College, Patna
- 2. SPECIAL THEORY OF RELATIVITY The position, and the time are relative physical quantities As these physical quantities are relative, motion is also relative. The theory which deals with the relativity of motion and rest is called the Theory of Relativity. It is divided into two parts. 1. Special Theory of Relativity, 2. General theory of relativity
- 3. The Special theory of relativity deals with objects or systems which are moving at a constant speed with respect to another or at rest. The general theory of relativity deals with objects or systems which are speeding up or slowing down with respect to one another. Frame of Reference: A well defined coordinate system which specifies the position and motion of the objects or systems is called Frame of Reference
- 4. A system relative to which the motion of any object is described is called a frame of reference. Or A well defined coordinate system, which can explain the motion of the objects, is called Frame of Reference. The motion of a body has no meaning unless it is described with respect to some well defined system.There are generally two types of reference systems: Inertial frames or un accelerated frames, Non-inertial frames.
- 5. Inertial Frames A frame of reference is said to be inertial when the objects in this frame obey Newton's law of inertia and other laws of Newtonian mechanics. In inertial frame, every object not acted upon by an external force, is at rest or moves with constant velocity. A frame of reference moving with constant velocity relative to an inertial frame is also inertial. Since, acceleration of the object in both the frames is zero, the velocity of the object is different but uniform.
- 6. Non-inertial frame: A frame of reference is said to be non-inertial when the objects in this frame do not obey Newton's law of inertia or Newton's laws of motion. In non-inertial frame, every object acted upon by an external force, is accelerated.
- 7. GALILEAN TRANSFORMATIONS: Galilean transformations are used to transform the coordinates of a particle from one inertial frame to another. They relate the observations of position and time made by two of observers, located in two different inertial frames. It is named after the Italian physicist Galileo Galilei, who first proposed it in the 17th century. Let us consider two inertial frames S and s' S is at rest and S' is moving with. a constant velocity v relative to S. Let an event is happening at point P at a particular time. Z
- 8. GALILEAN TRANSFORMATION : Let the coordinates of P with respect to S is (x,y,z,t) and with respect to S' is (x',y',z',t’). If t = t'= 0, the origins of the both reference frames coincides with each other S' frame travelled a distance of 'vt' after 't’ seconds Of time with respect to S frame. Let us choose our axes so that X and X' are parallel to v.Then the relation between these two frames can be written as x' = x – vt y' = y (there is no relative motion alongY and Z z' = z axes) t' = t (time is independent of space coordinate system) The above equations are known as Galilean transformations.
- 9. The inverse Galilean transformations can be expressed as under x = x' + vt y = y’ z = z’ t = t’ Galilean transformation for velocity can be written as: Galilean transformation for accelerationThe acceleration components can be obtained by differentiating velocity equations with respect to time. In vector form, a' = a Multiplying above equation with mass on both sides, we get ma' = ma F’=F The acceleration is same in both S and S' frames. So, acceleration and force are invariant in classical physics
- 10. APPLICATIONS OF GALILEAN TRANSFORMATION Planetary Motion: The Galilean transformation explains the motion of planets around the sun, treating their paths as simple, relative to a stationary reference frame. Moons Around Planets: It describes the motion of moons orbiting planets, using classical mechanics principles. Artificial Satellites: The motion of artificial satellites around Earth is explained using Galilean principles, assuming inertial frames. Objects in MovingVehicles: The transformation accounts for the motion of objects inside a moving car, assuming their behavior relative to the car's motion.
- 11. DRAWBACKS OF GALILEAN TRANSFORMATION The Galilean transformation fails to preserve the speed of light, making it appear different to observers in relative motion, unlike special relativity. It doesn't predict time dilation, where moving clocks run slower than stationary ones. The Galilean transformation doesn't account for length contraction, where moving objects appear shorter along the direction of motion. It assumes all inertial frames are equivalent, but special relativity shows the laws of physics differ between frames. Galilean transformation treats time and space as absolute, whereas special relativity shows they are relative to the observer's motion.
- 12. ThankYou! For your time and attention. Feel free to ask any questions! Presented by: Abhishek Kumar M.Sc (Physics) A.N. College, Patna