Posted by **Helen** on Sunday, December 4, 2011 at 1:43am.

A bowling ball of mass M and radius R is thrown along a level surface so that initially ( t= 0) it slides with a linear speed but does not rotate, see the figure. As it slides, it begins to spin, and eventually rolls without slipping.

How far has the ball moved down the lane when it starts rolling without slipping?

What are its final linear speed?

What are its final rotational speed?

Thanks:]

- Physics -
**drwls**, Sunday, December 4, 2011 at 2:15am
You need to specify kinetic friction coefficient and the initial velocity.

- Physics -
**Helen**, Sunday, December 4, 2011 at 2:23am
it says to answer it in terms of those coefficients

- Physics -
**Helen**, Sunday, December 4, 2011 at 2:25am
like, it's asking for formulas...

- Physics -
**Damon**, Sunday, December 4, 2011 at 4:39am
Initial w, angular velocity, is zero.

now while sliding

torque = I alpha

mu m g r = (2/5) m r^2 alpha

alpha = (5/2) mu g / r

and

F = m a

mu m g = m a

a = mu g

w = alpha t

v = Vi - a t

when does w r equal v (no slip)

r alpha t = v = Vi - a t

(5/2) mu g t = Vi - mu g t

(7/2)mu g t = Vi

so

t = (2/7)Vi/(mu g)

that is the time sliding

work back up to get distance and final v

Check that with energy argument:

frictional work done = mu m g d

Initial Ke - frictional work = Final Ke

(1/2) m Vi^2 - mu m g d = (1/2) m v^2 +(1/2) (2/5) m r^2 (v^2/r^2)

Vi^2 - 2 mu g d = (7/5)v^2

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