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

Step1: Recall the formula for linear velocity

The formula for linear velocity \(v = r\omega\), where \(r\) is the radius (distance from the center) and \(\omega\) is the angular velocity.

Step2: Compare the radii

Since the carousel is a rigid body, the angular velocity \(\omega\) is the same for all points on the carousel. Holly is at a larger \(r\) (near the outer edge) compared to Maria (\(r_{Holly}>r_{Maria}\)). Using \(v = r\omega\), when \(\omega\) is constant, \(v\propto r\). So, Holly has a greater linear velocity.

Part B

Step1: Recall the concept of angular velocity

Angular velocity \(\omega=\frac{\Delta\theta}{\Delta t}\), where \(\Delta\theta\) is the change in angular displacement and \(\Delta t\) is the change in time.

Step2: Analyze for a carousel

For a carousel (a rigid - body rotation), every point on the carousel (regardless of its distance from the center) has the same angular displacement \(\Delta\theta\) in the same time interval \(\Delta t\). So, \(\omega_{Holly}=\omega_{Maria}\)

Answer:

• Part A: Holly
• Part B: Neither (they have the same angular velocity)