Question

Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 4.06 kg and a radius of 0.253 m.

(a) Find the moment of inertia for each object as it rotates about the axes shown in this table.

hoop	___ kg · m2
solid cylinder	___ kg · m2
solid sphere	___ kg · m2
thin, spherical shell	___ kg · m2

(b) Suppose each object is rolled down a ramp. Rank the translational speed of each object from highest to lowest.

a) solid cylinder > thin spherical shell > solid sphere > hoop

b) solid sphere > solid cylinder > thin spherical shell > hoop     

c) hoop > solid cylinder > solid sphere > thin spherical shell

d) thin spherical shell > solid sphere > solid cylinder > hoop

(c) Rank the objects' rotational kinetic energies from highest to lowest as the objects roll down the ramp.

a) solid cylinder > thin spherical shell > solid sphere > hoop

b) hoop > thin spherical shell > solid cylinder > solid sphere    

c) hoop > solid cylinder > solid sphere > thin spherical shell

d) thin spherical shell > solid sphere > solid cylinder > hoop

Answer 1

a) moment of inertia of hoop = M R² = 4.06 * 0.253²= 0.259 kg.m²

moment of inertia of solid cylinder = 1/2 M R² = 1/2 * 4.06 * 0.253²= 0.129 kg.m²

moment of inertia of solid sphere = 2/5 M R² = 2/5 * 4.06 * 0.253²= 0.104 kg.m²

moment of inertia of thin spherical shell = 2/3 M R² = 2/3 * 4.06 * 0.253²= 0.173 kg.m²

b) b) solid sphere > solid cylinder > thin spherical shell > hoop

c) b) hoop > thin spherical shell > solid cylinder > solid sphere