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Ulleksa [173]
3 years ago
11

Suppose that a merry-go-round, which can be approximated as a disk, has no one on it, but it is rotating about a central vertica

l axis at 0.2 revolutions per second. If a 100kg man quickly sits down on the edge of it, what will be its new speed? (A disk has a moment of inertia I=(1/2)mR2 , mass of merry-go-round = 200kg , radius of merry-goround=6m)
Physics
1 answer:
seropon [69]3 years ago
4 0

Answer:

0.1 rev/s

Explanation:

M = mass of the merry go round = 200 kg

R = radius of merry go round = 6 m

I_{o} = Moment of inertia of merry go round = (0.5) MR² = (0.5) (200) (6)² = 3600 kgm²

m = mass of the man = 100 kg

I_{f} = Moment of inertia of merry go round when man sits on it at the edge = (0.5) MR² + mR² = (0.5) (200) (6)² + (100) (6)² = 7200 kgm²

w_{o} = initial Angular speed of merry-go-round before man sit = 0.2 rev/s

w_{f} = Angular speed of merry-go-round after man sit = ?

Using conservation of angular momentum

I_{o} w_{o} = I_{f} w_{f}

(3600) (0.2) = (7200) w_{f}

w_{f} = 0.1 rev/s

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