Question

Each of the following objects has a radius of 0.199 m and a mass of 2.35 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 38.1 rad/s. Find the magnitude of the angular momentum of each object.

(a) a hoop

(b) a solid cylinder

(c) a solid sphere

(d) a hollow spherical shell

Answer 1

given,

moment of inertia of hoop = MR^2

moment of inertia of hoop = 2.35 * 0.199^2

moment of inertia of hoop = 0.093 kg.m^2

magnitude of the angular momentum = moment of inertia * angular speed

magnitude of the angular momentum = 0.093 * 38.1

magnitude of the angular momentum = 3.5433 kgm^2/s

moment of inertia of solid cylinder = MR^2 / 2

moment of inertia of solid cylinder = 2.35 * 0.199^2 / 2

moment of inertia of solid cylinder = 0.0465 kgm^2

magnitude of the angular momentum = 0.0465 * 38.1

magnitude of the angular momentum = 1.77165 kgm^2/s

moment of inertia of solid sphere = (2/5) * MR^2

moment of inertia of solid sphere = (2/5) * 2.35 * 0.199^2

moment of inertia of solid sphere = 0.03722 kgm^2

magnitude of the angular momentum = 0.03722 * 38.1

magnitude of the angular momentum = 1.4181 kgm^2/s

moment of inertia of hollow sphere = (2/3) * MR^2

moment of inertia of hollow sphere = (2/3) * 2.35 * 0.199^2

moment of inertia of hollow sphere = 0.062 kgm^2

magnitude of the angular momentum = 0.062 * 38.1

magnitude of the angular momentum = 2.3622 kgm^2/s