Question

Two children, each with a mass of 25.4 kg, are at fixed locations on a merry-go-round (a disk that spins about an axis perpendicular to the disk and through its center). One child is 0.72 m from the center of the merry-go-round, and the other is near the outer edge, 3.07 m from the center. With the merry-go-round rotating at a constant angular speed, the child near the edge is moving with translational speed of 12.0 m/s.

(a) What is the angular speed of each child? ω 0.72 m = rad/s ω 3.07 m = rad/s

(b) Through what angular distance does each child move in 5.0 s? θ 0.72 m = rad θ 3.07 m = rad

(c) Through what distance in meters does each child move in 5.0 s? d 0.72 m = m d 3.07 m = m (d) What is the centripetal force experienced by each child as he or she holds on? Fc, 0.72 m = N Fc, 3.07 m = N

(e) Which child has a more difficult time holding on?

1.The outer child has a more difficult time holding on.

2.The inner child has a more difficult time holding on

Answer 1

Hi,

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PART (a):

Given that, Translational speed at the edge, V = 12 m/s

Radius of the disk, R = 3.07 m

Therefore angular speed of the disk is given by:

Angular speed is constant here.

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PART (b):

Time taken, t = 5 s

Therefore, Angular distance is given by:

Angular distance is also constant here.

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PART (c):

We have, angular distance,

Therefore, Distance in meters covered is given by:

Similarly:

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PART (d):

Centripetal force experienced by first child:

Similarly, Centripetal force experienced by second child:

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PART (e):

Centripetal force tends to push out the children from the merry-go-round.

Hence, the child having highest Centripetal force needs to hold strongly.

So, 1.The outer child has a more difficult time holding on.

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