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## Homework Statement

[/B]

A wheel with rotational inertia I = 1/2MR^2 about its horizontal central axle is set spinning with initial angular speed W

_{0}. It is then lowered, and at the instant its edge touches the ground the speed of the axle (and CM) is zero. Initially the wheel slips when it touches the ground, but then begins to move forward and eventually rolls without slipping.

How long does the wheel slip before it begins to roll without slipping?

## Homework Equations

V = v0+ at

f = ma

T = I*alpha

W = W0 + alpha*t

W*r = V

## The Attempt at a Solution

**Translational motion**

Fs = ma

-kmg = ma

a = -kg

V = v0 + at

V = -kgt

**Rotational motion**

Fs*r = I*alpha

kmgr = 1/2mr^2*alpha

alpha = 2kg/r

W = W

_{0}+ alpha*t

**Rolling without slipping condition**

W*r = V

W

_{0}*r + 2kgt = -kgt

-3kgt = W

_{0}r

t =

**-**W

_{0}r/(3kg)

My answer is correct if you don't see the minus sign. That probably means I couldn't draw the free body diagram properly. What should be the motion and the friction direction of the ball while it is slipping?

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