Question

Please show all work, thanks.

A beetle with a mass of 30.0 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 95.0 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 0.0800 rad/s clockwise with respect to the turntable.

(a) What does the turntable do while the beetle is walking?

The turntable remains at rest.

The turntable rotates clockwise, and with the same angular speed as the beetle's.

The turntable rotates clockwise, with a larger angular speed than the beetle's.

The turntable rotates clockwise, with a smaller angular speed than the beetle's.

The turntable rotates counter-clockwise, but with the same angular speed as the beetle's.

The turntable rotates counter-clockwise, with a larger angular speed than the beetle's.

The turntable rotates counter-clockwise, with a smaller angular speed than the beetle's.

(b) With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. rad/s

(c) 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

(d) If a mark is placed on the turntable at the beetle's starting point, how long does it take the beetle to reach the mark again? s

(e) Upon reaching the mark, the beetle stops. What does the turntable do?

To conserve angular momentum, the turntable slows down, but does not come to rest.

To conserve angular momentum, the turntable also comes to rest.

To conserve angular momentum, the turntable's angular velocity changes to the original angular velocity of the beetle.

To conserve angular momentum, the turntable keeps rotating at the same angular velocity.

To conserve angular momentum, the turntable reverses direction, but keeps the same angular speed.

To conserve angular momentum, the turntable speeds up.

Answer 1

Mass of beetle Mb = 30 g;

Mass of turn table Mt = 95 g;

angular speed of beetle wb = 0.0800 rad/s;

apply conservation of linear momentum;

0 = Mb*vb + (Mb + Mt)v;

v < 0 (negative) (ie The turntable rotates counter-clockwise, with a smaller angular speed than the beetle's.)

(b) wb =0.08 rad/s clockwise

apply conservation of angular momentum:

angular momentum lost by beetle = angular momentum gain by table

I_b*w_b = (I_b + I_t)w_t;

w_t = I_b*w_b/(I_b + I_t)

relative speed of beetal with respect to person watching = w_b - w_t > 0

clockwise

(c) angular velocity of the turntable wrt observer = counter clockwise