Sandra, of mass m s stand on the edge of a frictionless merry-go-round of radius
ID: 1288712 • Letter: S
Question
Sandra, of mass ms stand on the edge of a frictionless merry-go-round of radius R and the moment of inertia Icm that is not moving. She throws a rock of mass mr in a horizontal direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground is v.
a) what is the angular speed of the merry-go-round after the rock has been thrown?
b)What is the angular speed of the merry-go-round if, after throwing the rock, sandra walks inward to a radius of R/3 and sits down?
Explanation / Answer
initial angular momentum of rock + merry go+sandra L1 = 0
final angular momentum of rock = mr*v*R
final angular momentum of merry go = Icm*w
final angular momentum of sandra = ms*R^2*w
final angular momentum of rock + merry go +sandra
L2 = mr*v*R + Icm*w + ms*R^2*w
L2 =L1
mr*v*R + Icm*w + ms*R^2*w = 0
w = -(mr*v*R)/(Icm + ms*R^2)
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partb)
Icm*w + ms*R^2*w = Icm*w' + ms*R^2/9*w'
-mvR = Icm*w' + ms*R^2/9*w'
w' = (9*mr*v*R)/(9*Icm + ms*R^2)
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