# When do vcm=rw and a=gsintheta/(1+I/(MR)^2) apply?

## Homework Statement

Do the equations below only apply for rolling without slipping?

## Homework Equations

vcm=rw, a=(gsintheta)/(1+I/(MR)^2)
cm=center of mass

3. The Attempt at a Solution [/B]
I know that they both apply for rolling without slipping, but do they apply when there is slipping? Thank you.

haruspex
Homework Helper
Gold Member
Consider some simple examples of slipping - like a sphere sliding and not rotating at all. Does the first equation give the right answer?
I don't recognise the second equation. You'll need to describe the set up it applies to.

I see now. The equation vcm=rw would not apply if the ball was moving but not having rotational motion.

This is how I set up the equation:

Consider an object rolling down a inclined plane.

Torque=RFs
Also,
Torque=I*alpha
I=moment of inertia
alpha=angular acceleration
This leads to Torque = I*alpha=I*(a/R)
where a=acceleration centripetal

Setting RFs=I*(a/R) gives us Fs=(I*a)/R^2

So we have Fnet=ma=gravitational force down the incline plane-force of friction
which is=(mgsintheta)-(Ia)/R^2

Solving for a and manipulating the equation gives that a=(gsintheta)/(1+(I*alpha)/MR^2)

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