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March 27, 2015

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

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 2:15amYou need to specify kinetic friction coefficient and the initial velocity.

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

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

- Physics -
**Damon**, Sunday, December 4, 2011 at 4:39amInitial 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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