Question

A merry-go-round of radius R,shown in the figure, is rotating at constant angular speed. Thefriction in its bearings is so small that it can be ignored. Asandbag of mass mis dropped onto the merry-go-round, at a position designated byr.The sandbag does not slip or roll upon contact with themerry-go-round.
Rank the following different combinations of m and ron the basis of the angular speed of the merry-go-round after thesandbag "sticks" to the merry-go-round.
m= 10kg
r = .25 R
m= 15kg
r = .75 R
m=20kg
r = .25R
m=10kg
r = .5R
m= 40kg
r= .25R
m=10kg
r= 1.0R

Answer 1

conservation of angular momentum

I1ω1=I2ω2

I2 = I1 + mr^2

1)

mr^2 = 10/16

2)

mr^2 = 135/16

3)

mr^2 = 20/16

4)

mr^2 = 10/4 = 40/16

5)

mr^2 = 40/16

6)

mr^2 = 10 = 160/16

More mr^2 means more I2

More I2 means less ω2

The order is

6 < 2 < 4 = 5 < 3 < 1 (or) 1 > 3 > 5 =4 > 2 > 6