A merry-go-round of radius R,shown in the figure, is rotating at constant angula

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

Explanation / Answer

conservation of angular momentum

I11=I22

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 2

The order is

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

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