# rolling and sliding objects

Hi all!

I'm having some problems with rolling and sliding objects..

For example,
I have an homogeneous sphere with radius of 10 cm.
P=5N
It is moving in an horizontal and flat superficie until point A with
a constant velocity of 5m/s,
then from point A until point B the superficie is rough and the
coeficient of kinetic friction is 0.1.
In B the sphere start rolling without sliding.

The following diagram tries to explain the sphere path:

____A /\/\/\/\/\/\ B

The question is:

Find the kinetic energy in B

the mass of the sphere is iqual to 5/9.8 ~= 0.51
In B the sphere is not sliding and is only rolling, so that
Kinetic energy in B = Kinetic rotational energy in B = 1/2 I w^2

where I is the momentum of inertia that is equal to 2/5 M R^2

Ekb=1/2 *2/5 *M*R^2 * w^2
Ekb=1/5*0.51*0.1^2*w^2
Ekb=0.001 w^2

So, my problem is how can i found w?
i thouth in the formula v=w *r
But, in B the sphere is not sliding so, v = 0

Thanks,

Catarina Dias

.

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