Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical she
ID: 1367979 • Letter: F
Question
Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 5.05 kg and a radius of 0.243 m.
(a) Find the moment of inertia for each object as it rotates about the axes shown in this table.
(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
hoop ___kg · m2 solid cylinder ___ kg · m2 solid sphere ___kg · m2 thin, spherical shell ___ kg · m2Explanation / Answer
given,
mass = 5.05 kg
radius = 0.243 m
moment of inertia of hoop = mass * radius^2
moment of inertia of hoop = 5.05 * 0.243^2
moment of inertia of hoop = 0.298 kg.m^2
moment of inertia of solid cylinder = 0.5 * mass * radius^2
moment of inertia of solid cylinder = 0.5 * 5.05 * 0.243^2
moment of inertia of solid cylinder = 0.149 kg.m^2
moment of inertia of solid sphere= (2 / 5) * mass * radius^2
moment of inertia of solid sphere = (2 / 5) * 5.05 * 0.243^2
moment of inertia of solid sphere = 0.119 kg.m^2
moment of inertia of spherical shell= (2 / 3) * mass * radius^2
moment of inertia of spherical shell = (2 / 3) * 5.05 * 0.243^2
moment of inertia of spherical shell = 0.198 kg.m^2
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