# Rotational Inertia and Motion problems

Hello everyone, I am trying to solve some homework but I am not entirely sure what formulas to use.

Problem) There are 3 kids that weigh 25kg each sitting in the center of a merry go round (Disk). The merry-go-round weighs 400 kg and has a diameter of 3 m. It is initially spinning at 50 rpm.

A) What is the initial rotation?

I tried using the formula 1/2 mr^2. .5(400kg)(1.5)^2 = 450kg*m/s

B) What is the initial kinetic energy of the merry go round with the kids on it?
I tried 1/2 IW^2
1/2 (450)(5.2359878)^2 which equals 6168.5 N

W would be the 50 rpm converted to radians/second which would be 5.23rad/s and I was = 450 from earlier.

C) If all the kids move to the edge of the merry go round, what will be the new angular velocity in rad/s?

I got a little lost on this, would the proper formula be L = iw. 50 = 450w and w be the answer?

D) What is the magnitude of the linear velocity of each child as they sit on the edge and it spins at the rate round in C?

V = rω
V = 1.5(Answer from C in radians/sec)

E) The kids now want to stop. they drag their feet so they each exert a force F that is tangent to the disk in a direction that causes the merry-go-round to stop. How much net work must be done by the 2 kids in order to bring the disk with them on the edge to a stop.?

Not sure how to do this one.

F) If the disk stops after 6 seconds, what is the deceleration of the disk?
Wouldn’t this ω = ωo + (alpha)t
5.23(rad/s) = 0 + (alpha)(6)
5.23/6 = alpha?

G) What is the torque on the disk?
Not sure how to solve this one

H) Magnitude of the average Force F each kid needs to exert?
Not sure again how to solve this

I) How many revolutions will the disk need to turn before coming to a stop?

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