A sphere of mass m rolls on a plane surface. Find its kinetic energy at an instant when its centre moves with speed v.
A sphere having mass m rolls on a plane surface. Let its radius be R. Its center moves with a velocity v.
Therefore,
Kinetic energy = 12Iω2+12mv2
=12×(25mR2)×v2R2+12mv2
= 210mv2+12mv2
=(2+5)mv210=710mv2