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 4.19 kg and a radius of 0.239 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 · m2

Explanation / Answer

(a) the moment of inertia
hoop: I= MR² = 4.19 kg * (0.239 m)² = 0.239 kg·m²
solid cylinder: I= (1/2)MR² = 0.1196 kg·m²
solid sphere: I= (2/5)MR² = 0.0957 kg·m²
thin, spherical shell: I= (2/3)MR² = 0.1595 kg·m²

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

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

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