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# Angular Velocity?

A merry-go-round of radius R, shown in the figure, is rotating at constant angular speed. The friction in its bearings is so small that it can be ignored. A sandbag of mass m is dropped onto the merry-go-round, at a position designated by r. The sandbag does not slip or roll upon contact with the merry-go-round. How would you rank the following different combinations of m and r on the basis of the angular speed of the merry-go-round after the sandbag "sticks" to the merry-go-round from largest to smallest.

a) m = 10kg, r = 0.25R

b) m = 20kg, r = 0.25R

c) m = 10kg, r = 0.50R

d) m = 10kg, r = 1.0R

e) m = 15kg, r = 0.75R

f) m = 40kg, r = 0.25R

### 1 Answer

- RackbraneLv 71 decade agoFavorite Answer
The sandbag increases the moment of inertia I of the merry-go-round by approximately mr^2.

The bigger I becomes, the lower the angular speed becomes.

Values of mr^2/R^2 in kg are:

(a) 0.625 giving the largest angular speed after contact.

(b) 1.25

(c) & (f) 2.5

(e) 8.44

(d) 10 giving the smallest angular speed after contact.

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