2 [16 pts] Two children are riding a carousel. The girl is sitting on a horse 3

Question

2 [16 pts] Two children are riding a carousel. The girl is sitting on a horse 3 meters from the carousel's center. The boy is sitting on a horse closer to the edge of the carousel, farther from the center. The carousel completes 5 revolutions each minute. (a) Find the girl's tangential speed in m/s and her angular speed in rad/s tangential speed 1.57 m/s angular speed 0.52 rads (b) Find the girl's centripetal acceleration in m/s larger (c) Is the boy's tangential speed larger, smaller, or the same size compared to the girls' tangential speed? (d) Is the boy's angular speed larger, smaller, or the same sizs compared to the girls angular speed? (e) Is the boy's centripetal acceleration larger, smaller, or the same size compared to the girls' centripetal acceleration? larger same

Explanation / Answer

5 revolutions per minute is equal to 0.52359 rad/s

so

angular velocity = 0.523 rad/s

Girls tangential speed

V = R w = 3xw = 1.57 m/s

girls acceleration

a = w^2 R = 0.82 m/s^2

c)

speed is proportional to distance from center

so

boy is farther from center so his tangential speed will be more than girl ( larger )

d)

w is same for both ( same)

e)

acceleration is proportional to distance from center

so boy has larger acceleration( larger)

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