2. Dr. Lee Martin stands on a rotating platform that has an initial angular velo

Question

2. Dr. Lee Martin stands on a rotating platform that has an initial angular velocity of +3 rad/sec, where the positive vertical axis points upward. The moment of inertia of Dr. Martin plus the platform is 3.7 slug-ft2. Dr. Martin holds a spinning bicycle wheel with its axis horizontal. The wheel has a moment of inertia of 0.12 slug-ft2 and an angular velocity of +30 rad/sec. Determine the angular velocity of the platform for the following cases. Neglect the internal friction of the rotating platform.

A.The wheel is turned so the axis points straight up.(include units with answer)
Hint #1:Conservation of angular momentum.
B.The wheel is angled upward where the axis makes an angle of 46° from the horizontal.(include units with answer)
C.The wheel is turned so the axis points straight down.(include units with answer)
D.Dr. Martin reaches out and stops the wheel.(include units with answer)

Explanation / Answer

Appying angular momentum conservation,

(A) initial = final angular momentum

3.7 x 3 + 0.12 x 30 = (3.7 + 0.12) w

w = 3.85 rad/s ......Ans

(B) (3.7 x 3) + (0.12 x 30 x sin46) = (3.7 + 0.12) w

w = 3.58 rad/s

(C) (3.7 x 3) + (0.12 x -30) = (3.7 + 0.12) w

w = 1.96 rad/s

(D) (3.7 x 3) + (0.12 x 0) = (3.7 + 0.12)w

w = 2.91 rad/s

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