Chapter 10, Problem 51A

Megan rides a horse at the outer edge of a merry-go-round. She is located 6 m from the central axis and is a bit frightened of the speed. So her parents place her on a horse 3 m from the axis. While on the inner horse, how will her linear speed compare with her speed on the outer horse?

To determine

To Compare: The linear speed on the inner horse to that on the outer horse.

Answer to Problem 51A

The ratio of linear speed on the inner horse with that on the outer horse is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ .

Explanation of Solution

Given:

The distance from the central axis is 6 m and the distance of the horse from the central axis is 3 m.

Formula Used:

Linear speed is:

  $v=\omega \times r$

Here, $\omega$ is the angular speed, $r$ is the distance from the central axis.

As based on the above expression, velocity is directly proportional to the distance from the central axis.

  $v\propto r$

The radius becomes half as she moves from outer edge to inner edge. Thus, if the distance is reduced from 6 m to 3 m from the central axis thus the linear speed will also be reduced to half.

Conclusion:

Thus, the speed at inner horse will be half as that of outer horse.