Five objects of equal mass are shown below together with the axis about which th

Question

Five objects of equal mass are shown below together with the axis about which they are rotating. Select the objects in order of increasing rotational energy. If B has the smallest rotational energy, then A, C, D, and finally E with the largest rotational energy, enter BACDE (Note: If multiple objects have the same rotational energy, then enter them in the order they appear below.)The physical parameters of the various objects are on the printed assignment. A) Thin rod, about axis through center, perpendicular to the length with l = 7m and omega.gif=7rad/s B) Solid Cylinder, about cylinder axis with R = 3m and omega.gif=5rad/s C) Thin Spherical shell, about any diameter, with R = 2m and omega.gif=6rad/s (Note: Moment of inertia of such a thin shell is (2/3) M R^2) D) Solid Sphere, about any diameter, with R = 4m and omega.gif=5rad/s E) Thin cylindrical shell, about cylinder axis with R = 2m and omega.gif=5rad/s(Note: Moment of inertia of a thin cylindrical shell is the same as that of a thin hoop, just M R^2)

Explanation / Answer

Note that

KE = 1/2 I w^2

Let M = the mass of each object.

A.

I = 1/12 M L^2 = 4.083 M

Thus,

KE = 200.08 M

*************

B.

I = 1/2 M R^2 = 4.5 M

Thus,

KE = 112.5 M

*************

C.

I = 2/3 M R^2 = 2.6667 M

Thus,

KE = 96 M

**************

D.

I = 2/5 M R^2 = 6.4 M

Thus,

KE = 160 M

**************

E.

I = MR^2 = 4 M

Thus,

KE = 100 M

****************

Thus, we have CEBDA.

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