Reference Frames Galilean Transformations Quiz Outline

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

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.

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 ?

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

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?

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?

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

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