A thin uniform circular ring of mass and radius lies in the –plane with its centre at…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics
Problem
A thin uniform circular ring of mass M and radius R lies in the xy–plane with its centre at the origin.
(a) The ring has the same distribution of mass on all diameters. Justify why its moments of inertia about the x– and y–axes through the centre must be equal.
(b) Given that the moment of inertia of the ring about the axis through the centre perpendicular to the plane is Iz=MR2, use your result from part (a) to show that the moment of inertia about any diameter is 21MR2.
(c) If the ring rotates with angular speed ω about one of its diameters, obtain an expression for its rotational kinetic energy in terms of M,R, and ω. Comment on how this energy compares with the energy when it rotates with the same ω about the perpendicular axis through the centre.