Find the moment of inertia of a uniform sphere of mass and radius about an axis through its centre.
The kinetic energy of any rigid body with total mass , centre of mass , moment of inertia about an axis of rotation through , and angular velocity about that same axis, is given by . What physical interpretation can be given to the two parts of this expression?
A spherical marble of uniform density and mass rolls without slipping at speed along a flat surface. Explaining any relationship that you use between its speed and angular velocity, show that the kinetic energy of the marble is .