Question

two sisters want to ride the carousel at the amusement park. holly chooses a horse near the outer edge of the carousel. maria chooses a horse closer to the center.
part a
which sister experiences greater linear velocity?

part b
which sister has greater angular velocity?

Explanation:

• Part A: Linear velocity \(v = r\omega\), where \(r\) is the radius and \(\omega\) is the angular velocity. Since the carousel is a rigid body, \(\omega\) is the same for all points on the carousel. Holly's horse has a larger \(r\) (near the outer edge), so by \(v = r\omega\), Holly experiences greater linear velocity.
• Part B: Angular velocity \(\omega=\frac{\Delta\theta}{\Delta t}\). For a carousel (a rigid - body rotation), every point on the carousel rotates through the same angle \(\Delta\theta\) in the same time \(\Delta t\). So both riders have the same angular velocity.

Answer:

• Part A: Holly
• Part B: Both have the same angular velocity