A girl of mass (50 kg) stands on the rim of a frictionless merry-go-round (disk)

Question

A girl of mass (50 kg) stands on the rim of a frictionless merry-go-round (disk) of radius R = 2m and mass 200kg that is not moving. She throws a rock of m = 0.2kg horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock is 10 m/s relative to the ground. What is the angular momentum of the total system before throwing the ball? Is there any external torque? What is the angular momentum of the thrown ball to the rotation axis? What will be the angular momentum of the girl/merry-go-round? What will be the omega of the merry-go-round? What will be the girls linear speed?

Explanation / Answer

here,

mass of girl , m = 50 kg

radius of round , r = 2 m

mass of round , m1 = 200 kg

a)

the angular momentum of the system before the ball is through is zero as the system is at rest

b)

No, there is no external torque applied

c)

the angular momentum of the thrown ball w.r.t the rotation axis , Lb = mb * v * r

lb = 0.2 * 10 * 2 = 4 kg.m^2/s

d)

let the angular momentum of girl and round be Lg

using conservation of angular momentum

0 = Lg + Lb

Lg = - Lb = - 4 kg.m^2/s

e)

let the angular speed of merry go round be w

Lg = ( 0.5 * m1 * r^2 + m * r^2) * w

4 = ( 0.5 * 200 * 2^2 + 50 * 2^2) * w

w = 6.67 * 10^-3 rad/s

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