Question

Consider two kids spinning in circles on a merry-go-round. The first child is sitting three meters from the axis of rotation while the second is sitting six meters away. Which of the following is true?

Group of answer choices:

A) Both the tangential and angular velocity of the second child are twice as high as that of the first child

B) The tangential velocity of the second child is four times as high as that of the first but their angular velocities are the same

C) The tangential velocity of the second child is twice as high as that of the first but their angular velocities are the same

D) The two children have the same tangential and angular velocities

Answer 1

The angular velocities of two children on a merry-go-round are the same regardless of their distance from the center, while the tangential velocity is proportional to their distance from the axis of rotation, making the tangential velocity of the second child twice that of the first child.

Step-by-step explanation:

Considering two kids spinning on a merry-go-round, you are tasked with determining the relationship between their tangential and angular velocities based on their distance from the axis of rotation. The first important concept is that angular velocity is the same for any point on a rigid rotating body, which includes a merry-go-round. Therefore, regardless of how far the children are from the center, their angular velocities will be the same.

However, tangential velocity varies with the radius. Tangential velocity is calculated by multiplying the radius by the angular velocity. Given that the second child is twice as far from the center as the first child (6 meters compared to 3 meters), the tangential velocity for the second child is twice that of the first child if they are on the same rotating platform going at a constant angular velocity.

In conclusion, the correct answer is that the tangential velocity of the second child is twice as high as that of the first child, but their angular velocities are the same.