Question

part a

a girl and a boy are riding on a merry-go-round that is turning at a constant rate. the girl is near the outer edge, and the boy is closer to the center. who has greater linear speed?

• the girl has greater linear speed.
• both the girl and the boy have the same nonzero linear speed.
• the boy has greater linear speed.
• both the girl and the boy have zero linear speed.

Explanation:

Identify the rotational motion characteristics

Using the Rigid Body Rotation knowledge point

$$ \omega_{\text{girl}} = \omega_{\text{boy}} = \omega $$

Relate linear speed to angular speed

The linear speed \(v\) of a point on a rotating body is related to its distance \(r\) from the axis of rotation by:

$$ v = r \omega $$

Compare the distances and linear speeds

Since the girl is near the outer edge and the boy is closer to the center:

$$ r_{\text{girl}} > r_{\text{boy}} $$

Using \(v = r \omega\):

$$ v_{\text{girl}} > v_{\text{boy}} $$

Answer:

• The girl has greater linear speed. (Correct answer)
• Both the girl and the boy have the same nonzero linear speed.
• The boy has greater linear speed.
• Both the girl and the boy have zero linear speed.