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**1. Homework Statement**

A bowling ball is released without spin. How far does it travel before its motion is pure, rolling motion? No data is given, it asks for an order of magnitude estimate.

**2. Homework Equations**

k = mv^2/2

k = Iw^2/2 + mR^2w^2/2

I = 2MR^2/5

torque = Ialpha

torque = fk(R)

Work = fk(d)

V = Rw (w = omega, condition for rolling motion)

**3. The Attempt at a Solution**

The ball may slide a bit before it starts to roll at all. It will then roll and slide, then, eventually, only roll. There will be energy lost to friction. At the point the ball begins to roll (which is where V = Rw)

Krolling - Ksliding = -fk(d) or

Iw^2/2 + MR^2w^2/2 - Mv^2/2 = -fk(d)

Kinetic friction exerts a torque on the ball:

Ia = fk(R), and since Icm for a sphere is 2MR^2/5 and w = at

fk = 2MRt/5, substitute this in the above and simplify:

2Rw^2/5 + Rw^2/2 - V^2/2 = -2dt/5

and I think I just took a wrong turn some where :uhh:.

A gentle (or not so gentle) prod in the right direction would be very welcome right now.

Thanks so much,

Dorothy