A beetle with a mass of 20.0 g is initially at rest on the outer edge of a horiz

Question

A beetle with a mass of 20.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 75.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0700 rad/s clockwise with respect to the turntable. What is the angular velocity of the turntable (with respect to you)? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. (rad/s^2)

Explanation / Answer

The overall angular momentum must remain unchanged, thus the momentum of the beetle must cancel the momentum of the turntable.

Angular momentum is L = I

I for the disk is .5mdr2

I for the beetle is mbr2

so, .5mdr2d = mbr2b

The radii are the same for both since the beetle is on the outer rim of the dick, so r cancels, thus

.5(.075)(d) = (.020)(.07)

d = .0373 rad/s

Since the spin must be opposite to the beetle, it is counterclockwise, and your directions indicate that counterclockwise is negative, thus the angular velocity of the disk is -.0373 rad/s

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