An 800 kg merry-go-round with a diameter of 4.2 m is rotating freely with angula

Question

An 800 kg merry-go-round with a diameter of 4.2 m is rotating freely with angular velocity of ?o=0.80 rad/s. Four people, standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round.

a) Treating the people as "point masses", determine the new angular speed ?new of the merry-go-round after the four people step on.

One of the people now drags their foot on the ground, producing a constant friction force of FKF = 10.0 N tangent to the edge of the disk.

b) Determine the torque (magnitude and direction) created by this applied force.
c) How long will it take for the merry-go-round to come to rest?

Explanation / Answer

L1 = I1*W1 = 0.5*M*R^2*W = 0.5*800*2.1*2.1*0.8 = 1411.2 kg m^2 /s

L2 = (I1+I2)*W =( (0.5*800*2.1*2.1) + (4*65*2.1*2.1))*Wnew

L2 = L1

Wnew = 0.48 rad/s

b)torque T = r*f = 2.1*10 = 21 Nm

c) T = I*alfa = (I1+I2)*Wnew/t

t = 66.528 s

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