Understanding Tangential Speed on a Merry-Go-Round

Question:

Two children, Ralph and Jamal, ride on a merry-go-round. Ralph is at a greater distance from the axis of rotation than Jamal. Which of the following are true statements?

• A) Jamal has a greater tangential speed than Ralph.
• B) Ralph has a greater tangential speed than Jamal.
• C) Jamal and Ralph have the same tangential speed.

Answer:

The correct statement is: C) Jamal and Ralph have the same tangential speed.

Understanding Tangential Speed on a Merry-Go-Round

In a merry-go-round, all points on the ride move in a circular path around the axis of rotation. The tangential speed is the speed at which an object moves along the circumference of the circle.

Since both Ralph and Jamal are riding on the same merry-go-round, they are rotating with the same angular velocity, which means they complete one revolution in the same amount of time. Therefore, they have the same angular speed.

However, the distance from the axis of rotation affects the linear speed or tangential speed. The tangential speed is directly proportional to the distance from the axis of rotation. In this case, since Ralph is at a greater distance from the axis of rotation than Jamal, Ralph will have a greater linear speed or tangential speed compared to Jamal.

Therefore, option C is the correct statement: Jamal and Ralph have the same tangential speed.