Understanding Angular Velocity and Speed in Rotational Motion

What is the relationship between angular velocity and speed in rotational motion?

Which of the following statements is true?

A) They have different speeds and different angular velocities

B) They have the same speed, but their angular velocity is different

C) They have the same speed and the same angular velocity

D) They have the same speed and the same angular velocity, Final answer: B

Answer:

Sarah and Tom have the same speed, but their angular velocity is different.

When two objects are rotating at the same speed but have different radii, the one with the smaller radius will have a higher angular velocity. This can be understood by considering that the angular velocity is the rate at which an object rotates, while the linear velocity is the rate at which an object moves along the edge of the circular path.

Since Tom is halfway in from the edge of the merry-go-round, he has a larger radius compared to Sarah, who is sitting on the edge. Therefore, Sarah and Tom have the same speed, but their angular velocities are different.

The correct answer is B) They have the same speed, but their angular velocity is different.