A 4.2-m-diameter merry-go-round is rotating freely with an angularvelocity of 0.80 rad/s. Its total moment of inertia is1760kgm2. Four people standing on the ground, eachof mass 65 kg, suddenly step onto the edge of themerry-go-round. a. What is the angular velocity of themerry-go-round now? b. What if the people were on it initiallyand then jumped off in a radial direction (relative to themerry-go-round) ?

Answer

given,

mass of people = 65 kg

number of people =

diameter of the merry-go-round = 4.2 m

radius = 2.1 m

angular velocity = 0.8 rad/s

moment of inertia = 1760 kg m²

Using the law of conservation of angular momentum, we have

L₁ = L₂

I₁ω₁ = I₂ω₂

I₁ω₁ = (I₁ + 4 m r²) ω²

(1760 x 0.8) = (1760 + 4 x 65 x 2.12) ω²

1408 = 2311.2 ω²

ω² = 0.609

ω = 0.781 rad/s

b) If the people jump of the merry-go-round radially, they exert no torque.

hence, it will not change the angular momentum of the merry-go-round. It will continue to move with the same ω.