Asolid, uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m. what is the angular velocity of the sphere at the bottom of the inclined plane?

First of all, to work out the velocity at the bottom you can use the conservation of energy principle as friction isn't specified. So U = T or mgh = , rearranging to get . From this you get v = 11.72. Following angular velocity ω =  which you can use to get ω = 6.9. 

Hope that helps