A disk-shaped merry-go-round of radius 2.13 m and mass 145 kg rotates freely wit

Question

A disk-shaped merry-go-round of radius 2.13 m and mass 145 kg rotates freely with an angular speed of 0.681 rev/s . A 65.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim.

Part A

What is the final angular speed of the merry-go-round?

A disk-shaped merry-go-round of radius 2.13 m and mass 145 kg rotates freely with an angular speed of 0.681 rev/s . A 65.4 kg person running tangential to the rim of the merry-go-round at 3.51 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim.

Part A

What is the final angular speed of the merry-go-round?

Explanation / Answer

M = 145 kg , m = 65.4 kg , v = 3.51 m/s

w = 0.681 rev/s = 0.681*2*3.14 = 4.277 rad/s

r = 2.13 m

moment of inertia of disk = 0.5 Mr^2

from conservation of angular momentum

I1w1 = I2w2

(0.5Mr^2)w1+ mvr = (0.5M^2 +mr^2)w2

(0.5*145*2.13^2)(4.277) +(65.4*3.51*2.13) = ((0.5*145*2.13^2) +(65.4*2.13^2))w2

w2= 3.03 rad/s

w2= 3.03/6.28 = 0.482 rev/s

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