A 30 kg kid is standing halfway to the edge of a 50 kg spinning merry-go-round (

Question

A 30 kg kid is standing halfway to the edge of a 50 kg spinning merry-go-round (MgR) with a radius of 1.2 m. The kid and the MgR are spinning at 4.5 rad/s.

a. What can the kid do to slow down the rotation of the MgR platform?

b.What can the kid do to speed up the rotation of the MgR platform?

c. What can the kid do while standing on the MgR to change the angular momentum of the kid-MgR system?

d. Find the rotational speed of the platform if the kid moves to the outer edge of the MgR.

e. Now, find the rotational speed of the platform is the kid starts to run at 1.5 m/s along the outer edge of the platform in the direction of his rotation.

f. The kid now turns around and runs the other direction, so that he appears to be at rest to an observer standing on the ground. What is the speed of the MgR platform?

Explanation / Answer

conservation of angular momentum I*w=constant i,e. MR^2 w = constant

I=moment of inertia, w = angular speed

a) From the conservation of angular momentum we can say, that the kid should go towards outer edge to slow down the rotation of MGR platform.

b)From the conservation of angular momentum we can say, that the kid should go towards the center to speed up the rotation of MGR platform.

c) To change the angular momentum of the kid MGR system the kid should go either towards edge or towards center.

d) Mkid = 30 kg M=50 kg radius r =1.2 m w=4.5 rad/s when kid is standing midway.

I= Mkid(r/2)^2 + Mr^2/2 when kid is standing midway.

=46.8 kg-m^2

I' = Mkid*r^2 + Mr^2/2 when kid is standing at the edge.

= 79.2 kg-m^2

Iw = I'w'

w' = (Iw)/I'

=(46.8*4.5)/79.2

=2.66 rad/s

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