Two ladybugs sit on a rotating disk that is slowing down at a constant rate. The ladybugs are at rest with respect to the surfac

Question

2 years ago

8

Two ladybugs sit on a rotating disk that is slowing down at a constant rate. The ladybugs are at rest with respect to the surfac

e of the disk and do not slip. Ladybug 1 is halfway between ladybug 2 and the axis of rotation. How does the rotational speed of ladybug 1 compare to ladybug 2?

Physics

1 answer:

d1i1m1o1n [39] · Answer 1 · 2022-07-28T13:07:29+03:00

The two ladybugs have same rotational (angular) speed

Explanation:

The rotational (angular) speed of an object in circular motion is defined as:

$\omega=\frac{\theta}{t}$

where

$\theta$ is the angular displacement

t is the time interval considered

Here we have two ladybugs, which are located at two different distances from the axis. In particular, ladybug 1 is halfway between ladybug 2 and the axis of rotation. However, since they rotate together with the disk, and the disk is a rigid body, every point of the disk cover the same angle $\theta$ in the same time $t$ : this means that every point along the disk has the same angular speed, and therefore the two ladybugs also have the same angular speed.

On the other hand, the linear speed of the two ladybugs is different, because it follows the equation:

$v=\omega r$