Galilean Transformation Equations

Introduction - Galilean Transformation equations

1. B.Raju Dept.of Physics., KGC Hanamkonda Special Theory of Relativity-Lecture– 1 B.Sc. Physics - First Year - First Semester Topic: Introduction- Galilean Transformations

2. Dept.of Physics., KGC Hanamkonda 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. Dept.of Physics., KGC Hanamkonda . 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. Dept.of Physics., KGC Hanamkonda 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 . X Y Z O P ( x ,y , z ) . 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: 1 . Inertial frames or un accelerated frames , 2. Non-inertial frames.

5. Dept.of Physics., KGC Hanamkonda 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 . Inertial Frames:

6. Dept.of Physics., KGC Hanamkonda 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. Dept.of Physics., KGC Hanamkonda 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. Let us consider two inertial frames S and . S is at rest and is moving with a constant velocity v relative to S. Let an event is happening at point P at a particular time S Y Z X O v . P x vt

8. Dept.of Physics., KGC Hanamkonda GALILEAN TRANSFORMATIONS: S Y Z X O v . P x vt 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 .

9. Dept.of Physics., KGC Hanamkonda L et us choose our axes so that X and X’ are parallel to v. Then the relation between these two frames can be written as ( there is no relative motion along Y and Z axes ) ( time is independent of space coordinate system ) The above equations are known as Galilean transformations.

10. Dept.of Physics., KGC Hanamkonda The inverse Galilean transformations can be expressed as under Galilean transformation for velocity can be written as:

11. Dept.of Physics., KGC Hanamkonda Galilean transformation for acceleration The acceleration components can be obtained by differentiating velocity equations with respect to time. In vector form, a ˈ = a Multiplying above equation with mass on both sides, we get ma ˈ = ma

12. Dept.of Physics., KGC Hanamkonda F ˈ = F The acceleration is same in both S and S ’ frames. So, acceleration and force are invariant in classical physics . Drawbacks of Galilean Transformations: 1.The laws of electromagnetism or electrodynamics and Maxwell’s equations are not invariant under Galilean transformations. 2.Galilean transformations are invalid when the objects are moving with nearer velocities of velocity of light.

13. Dept.of Physics., KGC Hanamkonda ASSIGNMENT 1.What is theory of relativity and explain 2.Define frame of reference 3.Distinguish between inertial and non inertial frames 4.Derive Galilean Transformation equations, and write its drawbacks THANK YOU