Question

A rhinoceros beetle rides the rim of a horizontal disk rotating counterclockwise like a merry-go-round. If the beetle then walks along the rim in the direction of the rotation, will the magnitudes of the following quantities (each measured about the rotation axis) increase, decrease, or remain the same (the disk is still rotating in the counterclockwise direction): (a) the angular momentum of the beetle–disk system, (b) the angular momentum and angular velocity of the beetle, and (c) the angular momentum and angular velocity of the disk? (d) What are your answers if the beetle walks in the direction opposite the rotation?

Short answer

a) Angular momentum of the beetle-disk system will remain the same.

b) Angular momentum and angular velocity of the beetle will increase.

c) Angular momentum and angular velocity of the disk will decrease.

d) When the beetle walks in the opposite direction of the rotation, the angular momentum of the beetle-disk system will remain the same, its angular momentum and angular velocity of the beetle will decrease while that of the disk will increase.

Step-by-step solution

Step 1: Given

Horizontal disk rotating counter-clockwise with a beetle on it.

Determining the concept

Use the concept of angular momentum and angular velocity. There is a proportional relation between the angular velocity and linear velocity.

The formula is as follows:

$L=I\omega$

WhereL is angular momentum, I is a moment of inertia and $\omega$is angular velocity.

(a) Determining the angular momentum of the beetle-disk system

When a beetlewalks along with a disk in the direction of rotation, it will have a little more angular velocity but it will decrease the angular velocity of the disk, so finally, the angular momentum of the beetle and disk remains the same.

(b) Determining the angular momentum and angular velocity of the beetle

In this case, if seen separately, beetles will have more angular velocity and hence the angular momentum. But for a disk, the angular velocity decreases little and so does the angular momentum.

(c) Determining the angular momentum and angular velocity of the disk

If the beetle walks opposite the direction of rotation the angular momentum and velocity of the beetle will decrease while the angular momentum and angular velocity of the disk will increase.

(d) Determining what will happen when the beetle walks in the opposite direction of the rotation

Whether the angular momentum and angular velocity increase, decrease, or remain the same can be found depending on the direction of the motion of the object.

When the beetle walks in the opposite direction of the rotation, the angular momentum of the beetle-disk system will remain the same, its angular momentum and angular velocity of the beetle will decrease while that of the disk will increase.