15. -/2 points FRKestenCP18.P. 117 My Notes + A 502-kg merry-go-round (a flat, s

Question

15. -/2 points FRKestenCP18.P. 117 My Notes + A 502-kg merry-go-round (a flat, solid cylinder) supports 8 children, each with a mass of 49 kg, located at the axis of rotation (thus you may assume the children have no angular momentum at that location). Describe a plan to move the children such that the angular velocity of the merry-go-round decreases to one-half its initial value. (Find the distance from the center the children would have to be in terms of the radius of the merry-go-round.) Rchild= RMGR eBook

Explanation / Answer

initial angular momentum Li = I*wi

I = moment of inertia of merry go round I = (1/2)*M*RMGR^2

after the children moved to a distance r

final angualr momentum Lf = ( I + (8*m*Rchild^2))*wf

wf = wi/2

from moemntum conservation

Lf = Li

((1/2)*502*RMGR^2*wi = ((1/2)*502*RMGR^2 + (8*49*Rchild^2))*wi/2

((1/2)*502*RMGR^2 = ((1/2)*502*RMGR^2 + (8*49*Rchild^2))*1/2

(1/2)*502*RMGR^2 = (1/4)*502*RMGR^2 + 196*Rchild^2

125.5*RMGR^2 = 196*Rchild^2

Rchild^2 = (125.5/196)*RMGR^2

Rchild = 0.8*RMGR

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