I\'m in an algebra-based physics class, so please use those methods. I really wa

Question

I'm in an algebra-based physics class, so please use those methods. I really want to learn the steps to study so please show each step (even if it seems like an easy one - algebra doesn't come easy to me). Thanks in advance!

(a) A 15.0 kg child is riding a playground merry-go-round that is rotating at 35.0 rpm. What centripetal force must she exert to stay on if she is 3.00 m from its center? Answer in N.
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 8.00 m from its center? answer in N.
(c) Compare each force with her weight.
Answer 1 (force from part (a) / weight)
Answer 2 (force from part (b) / weight)

Explanation / Answer

given radius r1 = 3 m

angular speed = w1 = 35 rpm = 35*(2*pi/60) = 3.66 rad/s

centripetal force F1 = m*r1*w1^2 = (15*3*3.66^2) = 602.8 m/s^2

(b)

radius = 8 m

speed = 2 rpm = 3*(2pi)/60 = 0.314 rad/s

centripetal force F2 = m*r2*w2^2

F2 = 15*8*0.314^2 = 11.83 N

(c)

F1/mg = 4.1

F2/mg = 0.08

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