Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical she

Question

Four objects—a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell—each have a mass of 4.46 kg and a radius of 0.184 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

Explanation / Answer

a) the moment of inertia
hoop: I= MR² = 4.46 kg (0.184 m)² = 0.151 kg·m²
solid cylinder: I= (1/2)MR² = 0.0755 kg·m²
solid sphere: I= (2/5)MR² = 0.0604 kg·m²
thin, spherical shell: I= (2/3)MR² = 0.1 kg·m²

(b)
B)solid sphere > solid cylinder > thin spherical > hoop

(c)
B)hoop > thin spherical > solid cylinder > solid sphere

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