In a playground, there is a small merry-go-round of radius 5.00 m and mass 230 k

Question

In a playground, there is a small merry-go-round of radius 5.00 m and mass 230 kg. Its radius of gyration is 3.80 m. A child of mass 36.0 kg runs at a speed of 1.70 m/s along a path that is tangent to the rim of the initially stationary merry-go-round and then jumps on. Neglect friction between the bearings and the shaft of the merry-go-round. Calculate (a) the rotational inertia of the merry-go-round about its axis of rotation, (b) the magnitude of the angular momentum of the running child about the axis of rotation of the merry-go-round, and (c)the angular speed of the merry-go-round and child after the child has jumped on.

Explanation / Answer

(a)

inertia = I = m*k^2 = 230*3.8^2 =3321.2 kg m^2

(b)

L = m*v*r = 36*1.7*5 = 306 kgm^2/s

c)

angular momentumof merry go round

L = I*w

306 = 3321.2*w

w = 0.092 rad/s

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