All Problems

Dynamics of a solid body

Problem 1.263

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.

Reveal Answer
ω=10g(R+r)/17r2\omega=\sqrt{10 g(R+r) / 17 r^{2}}