A uniform ball of radius r rolls without slipping down from the top of a sphere of radius R , find the angular velocity of the ball at the moment it breaks off the sphere . The initial velocity of the ball is negligible .

Question

anonymous · Answer

do u know the answer ( not solution)

anonymous · Answer

the velocity of the body is V (same as that of centre of mass)
so V=r*W(omega)
so find omeaga

anonymous · Answer

The moment it breaks off the sphere indicates that the normal force is equal to zero and all the centripetal acceleration is due to gravity. So find an equation that relates normal force, gravity, and centripetal acceleration. You need to use an angle theta to fully describe it all. 

Then you will have two unknowns, the angle at which this all happens, and the velocity of the ball. Describe the velocity in terms of something more useful with the help of the conservative force of gravity (using potential and kinetic energy of the ball at different heights). 

You will have two equations with two unknowns so things will make sense.

I believe this is the right approach, and I did not want to get too into detail.

anonymous · Answer

@hemanoman the moment the ball slips it is no longer having centripetal acc as it is no more moving in a circle but just flys out tangentially to the sphere