A uniform thin rod of length 0.95 m and mass 1.2 kg lies in a horizontal plane a

Question

A uniform thin rod of length 0.95 m and mass 1.2 kg lies in a horizontal plane and rotates in that plane about a pivot at one of its ends. The rod makes one rotation every 0.39 second and rotates clockwise as viewed from above its plane of rotation. A)Find the magnitude of the rod’s angular momentum about its rotation axis, in units of kgm^/s.

b) find the rotational kinetic energy, in joules, of the rod described in part (a). c) a thin-walled hollow sphere of radius 0.57 m and mass 1.5 kg rotates about a vertical axis through its center. The sphere makes one rotation every 0.38 second and rotates counterclockwise as viewed looking down from above. Find the magnitude of the sphere’s angular momentum about its rotation axis, in units of kgm^2/s. d) find the rotational kitetic energy, in joules, of the sphere described in part c.

Explanation / Answer

(A) w = 2pi / T =16.1 rad / s

I = m L^2 / 3 =0.361 kg m^2

L = I w = 5.81 kg m^2 / s

(B) KE = I w^2 / 2 = 1.05 J

(C) w = 2pi / T = 16.53 rad/s

I = 2 m r^2 / 3 = 0.325 kg m^2

L = I w = 5.37 kg m^2 / s

(D) KE = I w^2 / 2 =0.284 J

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