Which radius (r or R) should you use? Why?

[shimizua]

Homework Statement

A rolling wheel of radius r has translational velocity v as well as angular velocity w. Here you will relate translational velocity to angular velocity. Since the circumference of a circle of radius r is 2p r, every time the center of mass moves a distance 2p r, the object rotates a full circle (2p radians). If this happens in a time T then
v = Dx/Dt = 2p r / T (1)
and w = Dq/Dt = 2p/T (2)
Combine these equations to find an expression for w in terms of v.

2.When applying equation 1 (in question 1) to our system, which radius (r or R) should you use? Why?

Homework Equations

so i figured out the first question, i was just putting it up so you knew what was going on. But as far as equations i don't think there would be any for this question

The Attempt at a Solution

I think it should be r since in the equation and statement they only refer to r and not R

 

[jgens]

Just divide the two equations and solve the resulting equation for w.

 

[thomate1]

. R may be the radius of the entire wheel, but since we are talking about the center of mass and rotational motion, r should be used.