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1. A disk (I=MR^2 M= 150 Kg R= 3m) rotates at 7 m/s. Then a uniform disk with M=

ID: 1293218 • Letter: 1

Question

1. A disk (I=MR^2 M= 150 Kg R= 3m) rotates at 7 m/s. Then a uniform disk with M= 50 kg and R= 2m initially at rest is dropped onto the original disk. They are both rotating on the same axis. What is the angular velocity after the collision?

2. A merry-go round that is a disk (I=MR^2, M= 600 kg, R= 2.5m) is at rest. A child with mass of 45 kg is running at a velocity of 11 m/s tangentially to the merry-go-round. He approaches the merry-go-round and steps on. What is the final angular velocity of the merry-go-round?

Explanation / Answer

initial angular momentum Li = (1/2)*M1*R1^2*w1


Li = (1/2)*M1*R1^2*V/R1 = (1/2)*M1*R1*v1

Li = (1/2)*150*3*7 = 1575 kg m^2 /s

final angular momentum

Lf = [(1/2)*M1*R1^2 + (1/2)*M1*R2^2 ] w2


Lf = [((1/2)*150*3*3) + ((1/2)*50*2*2)) ] *w2


Lf = 7758w


from momentum conservation Lf = Li


775*w2 = 1575

w2 = 2.0322 rad/s


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2) Li = m*v*R = 600*11*2.5 = 16500 kg m/s^2


Lf = (I + m*R^2)w

Lf = [((1/2)M*R^2) + m*R^2 ]*w

Lf = ((1/2)*600*2.5*2.5) + (45*2.5*2.5) *w


Lf = 2156.25*w


Lf = Li


2156.25*w = 16500


w = 7.652 rad/s