Four objects - a hoop, a solid cylinder, a solid sphere, and a thin, spherical shell - each has a mass of 4.59 kg and a radius of 0.252 m.

(a) Find the moment of inertia for each object as it rotates about the axes shown in the table above.
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 > solid sphere > hoop

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

C)hoop > solid cylinder > solid sphere > thin spherical

D)thin spherical > 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 > solid sphere > hoop

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

C)hoop > solid cylinder > solid sphere > thin spherical

D)thin spherical > solid sphere > solid cylinder > hoop

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  1. I figure it out

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  2. (a) You should take the time to look these up.
    I(hoop) = M R^2
    I(solid sphere) = (2/5) M R^2
    I(solid cylnder) = (1/2) MR^2
    I(spherical shell) = (2/3) MR^2

    (b) The higher the value of (I/MR^2), the slower it rolls, because more of the potential energy is used up making it spin. You do the ranking

    (c) The order will be opposite from (b)

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