A child is standing at the center of a playground merry-go-round that is making

Question

A child is standing at the center of a playground merry-go-round that is making 35 rotations per minute. You can approximate the merry-go-round as a disk of radius 1.4 meters and mass 115 kg.

a.) What is the angular velocity in rad/sec?

b.) What is the moment of inertia?

c.) What is the angular momentum?

Now the child (mass of 33 kg) moves from the center to the edge of the merry-go-round.

d.) What is the angular momentum now?

e.) What is the moment of inertia now?

f.) What is the angular velocity now?

Explanation / Answer

here,

radius , r = 1.4 m

mass of ground , m = 115 kg

a)

the angular velocity , w = 35 rpm

w = 35 *6.28/60 rad/s

w = 3.66 rad/s

b)

moment of inertia , MI = 0.5 *m * r^2

MI = 0.5 * 115 * 1.4^2

MI = 112.7 kg.m^2

the moment of inertia is 112.7 kg.m^2

c)

the initial angular momentum , L = MI*w

L = 112.7 * 3.66

L = 412.48 kg.m^2/s

d)

using conservation of angulr momentum

the angular momentum remains constant

the final angular momentum is 412.48 kg.m^2/s

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