Question

Consider a string with several rocks tied along its length at equally spaced intervals. You whirl the string overhead so that the rocks follow circular paths. Compared to a rock in the middle of the string, a rock at the outer end moves
A) half as fast.
B) twice as fast.
C) at the same linear speed.

Answer 1

Answer:

(B) twice as fast.

Explanation:

The speed of an object in circular motion can be expressed as follows;

Speed = distance / time                         -Equation (1)

The distance in turn can be expressed (in radians) as:

Distance = radius * (change of angle in radians)                 -Equation (2)

Since the change of angle is equal, because of equal angular speed of the rocks, the speed only depends on the radius of the rock from the center.

Combining equation 1 and 2, we get:

Speed = (radius * change in angle) / time

We can see here that if radius is increased by two, the speed increases by two as well. So our answer is (B)