Ben and Jerry are standing at the center of a 134 kg merry-go-round of radius 1.

Question

Ben and Jerry are standing at the center of a 134 kg merry-go-round of radius 1.30 m that is already spinning at 3.00 rad/s. They proceed to walk in opposite directions toward the edge of the merry-go-round.

If Ben reaches the edge while Jerry is halfway between the center and the edge, what will be the new angular velocity (in rad/s) of the merry-go-round? Assume Ben and Jerry can be modeled as point masses of 32.0 kg and 21.0 kg, respectively, and that the merry-go-round can be modeled as a disk rotated about its axis.

Explanation / Answer

Using Angular momentum

Li = Lf

Ii*wi = If*wf

wf = wi*(Ii/If)

moment of inertia of disk = M*R^2/2

Moment of inertia of Ben/Jerry about center of disk = m*r^2

where r = distance from center

Ii = M*R^2/2 + 0 + 0

Since initially Ben And Jerry are at center, so r = 0

Ii = 134*1.30^2/2 = 113.23 kg-m^2

wi = 3 rad/sec

If = MR^2/2 + mb*rb^2 + mj*rj^2

mb = mass of ben = 32 kg

mj = mass of jerry = 21 kg

rb = distance of ben from center = R = 1.30 m

rj = distance of jerry from center = R/2 = 0.65 m

If = 134*1.30^2/2 + 32*1.30^2 + 21*0.65^2

If = 176.18 kg-m^2

Now

wf = 3*(113.23/176.18)

wf = 1.93 rad/sec

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