All Problems

Dynamics of a solid body

Problem 1.267

A uniform sphere of mass \(m\) and radius \(r\) rolls without sliding over a horizontal plane, rotating about a horizontal axle \(O A\) (Fig. 1.70). In the process, the centre of the sphere moves with velocity \(v\) along a circle of radius \(R\). Find the kinetic energy of the sphere.

Reveal Answer
T=7/10mv2(1+2/rr2/R2)T=7 /_{10} m v^{2}\left(1+2 / r r^{2} / R^{2}\right)