Question

A marching band consists of rows of musicians walking in straight, even lines. When a marching band performs in an event, such as a parade, and must round a curve in the road, the musician on the outside of the curve must walk around the curve in the same amount of time as the musician on the inside of the curve. This motion can be approximated by a disk rotating at a constant rate about an axis perpendicular to its plane. In this case, the axis of rotation is at the inside of the curve.Consider two musicians, Alf and Beth. Beth is four times the distance from the inside of the curve as Alf.

Knowing that If Beth travels a distance s during time Δt, how far does Alf travel during the same amount of time= (1/4)s

If Alf moves with speed v, what is Beth's speed? Speed in this case means the magnitude of the linear velocity, not the magnitude of the angular velocity.

a)4v b) v c) v/4

Answer 1

Angular velocity is equal to,

$v = \omega r$

If angular velocity is constant then magnitude of linear velocity is directly proportional to radius of curve,

hence magnitude of the linear velocity of beth is 4v.