Understanding Galilean Transformations and Inertial Reference Frames

1. Outline Reference Frames • Galilean Transformations • Quiz

2. Galileo’s Principle of Relativity • A coordinate system specifies direction vectors • The coordinate system may be moving • Inertial coordinate systems are not accelerating • An inertial coordinate system is called an inertial reference frame • Newton’s laws hold true in an inertial (non- accelerating) reference frame

3. Transformation of position x‘ x P path plotted in xy co-ordinates y’ y • The position a particle P is described by in (x,y) • The same particle is described by in (x’,y’) • connects the origins of the two coordinate systems.

4. QQ52:position transform Example: In your reference frame, x’y’, you see a student at position vector: Your reference frame has its origin at: with respect to my frame. What is the student’s position in my frame ?

5. What if the reference frames are moving? x‘ x P path plotted in xy co-ordinates y’ y  

6. QQ53:velocity transform Example: In your reference frame, you see a student moving with a velocity given by: In my reference frame, I see the same student moving with a velocity given by: What is my velocity relative to you?

7. QQ52:position transform Example: You are in a car moving at 10m/s. You throw a ball at 5m/s in the direction of the car’s motion. a) what is the ball’s speed wrt to the car?b) what is the ball’s speed wrt a stationary person?

8. Galilean Principle of Relativity  An Inertial Reference Frame is one in which is a constant, do dV/dt=0:  

9. Forces in Frames Because: If you apply a force in one frame, the object will accelerate at the same rate in both frames and. Hence, if a=(2i+3j) m/s2 then a’= =(2i+3j) m/s2