A thin circular ring (hoop) and a uniform solid disc each have mass and radius
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A thin circular ring (hoop) and a uniform solid disc each have mass 2kg and radius 0.30m. Both rotate freely about their symmetry axes (perpendicular to their planes through the centres) with an angular speed of 20rad s−1. Answer the following.
(i) State the expression for the rotational kinetic energy of a rigid body in terms of its moment of inertia and angular speed.
(ii) Using standard values of moment of inertia, calculate the rotational kinetic energy of the ring and of the disc.
(iii) Which body possesses the larger rotational kinetic energy? By what factor is it greater than the other?
(iv) Keeping the rotational kinetic energy of the ring unchanged, determine the angular speed required for the disc so that its rotational kinetic energy equals that of the ring.