3. Jack and Jill now head towards the merry-go-round for some fun. They each sit

Question

3. Jack and Jill now head towards the merry-go-round for some fun. They each sit 0.850 m out from the center. Someone comes along and gives the merry-go-round a push, getting it spinning at a rate of 14.0 rpm. (Assume the friction and air resistance are negligible in slowing down the merry-go-round. Parts a-e, assume that friction between the children and the surface of the merry-go-round is sufficient to keep the children in place). (5 points) a. What is the angular speed of Jack (in rad/s)? b. What is the angular speed of Jill (in rad/s)? c. What is the tangential speed of Jack (m/s)? d. What is the tangential speed of Jill (in m/s)? e. If both Jack and Jill scoot closer in towards the center (to 0.642 m), what will happen to the rotational speed of the merry-go-round? Find the angular speed at their new location. (Hint: use conservation of angular momentum!) f. What is the coefficient of static friction needed between the kids and the merry-go-round to keep both kids on the ride?

Explanation / Answer

a. 14/(60*0.85) =0.2745 rad/s

b. 0.2745 rad/s

c. v=wr=0.233 m/s

d. 0.233 m.s

e. conserving angular momentum

Iw=constant.

w=0.48 rad/s

rotation speed = 18.48 rpm

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