Rotational Motion: Meaning of ∫v(t)dt - ∫Rw(t)dt

[gsimo1234]

This is merely a simple, but conceptual, problem. Say we have a cue ball of mass M and Radius R rolling without slipping on the pool table. What is the the meaning of the ∫v(t)dt - ∫Rw(t)dt where w(t) is the angular speed of the pool ball.

My guess is that this represents the length the ball has moved and the amount of radians that the ball has spun through. Am I correct?

 

[kuruman]

You are correct about the first integral but not the second. Do dimensional analysis and you will see why.