A playground merry-go-round with a mass of 145 kg and a radius of 2.1 m is rotat

Question

A playground merry-go-round with a mass of 145 kg and a radius of 2.1 m is rotating with a frequency of0.44 rev/s.

Randomized Variablesm1 = 145 kg
m2 = 27 kg
?i = 0.44 rev/s
r = 2.1 m 100% Part (a) What is the magnitude of its angular velocity, in radians per second, after a 27 kg child gets onto it by grabbing its outer edge? The child is initially at rest. A playground merry-go-round with a mass of 145 kg and a radius of 2.1 m is rotating with a frequency of0.44 rev/s. Randomized Variablesm1 = 145 kg m2 = 27 kg ?i = 0.44 rev/s r = 2.1 m 100% Part (a) What is the magnitude of its angular velocity, in radians per second, after a 27 kg child gets onto it by grabbing its outer edge? The child is initially at rest.

Explanation / Answer

Initial moment of inertia (solid disk) Ii = 0.5*M*r^2 = 0.5*145*2.1^2 = 319.725 kg.m^2
Initial angular velocity ?i = 0.400*2pi rad/s = 2.512 rad/s

Angular momentum = Ii*?i = 803.15 kg.m^2/s = constant

Child moment of inertia (point mass) = m*r^2 = 27*2.1^2 = 119.07 kg.m^2

Final moment of inertia If = 319.725+119.07= 438.795 kg.m^2

So final speed is ?f = 803.15 / 438.795 rad/s =1.83 rad/s Ans.

or 1.83 / 2pi = 0.2914 rev/s

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