A 30kg girl is sitting at the edge of a 200kg merry-go-round with a radius of 1.

ID: 1307670 • Letter: A

Question

A 30kg girl is sitting at the edge of a 200kg merry-go-round with a radius of 1.5m. A 10kg

cannonball is fired at the girl in a direction tangent to the edge of the merry-go-round at which

the girl is sitting. The initial speed of the cannonball is 15m/s. The girl catches the cannonball,

and remains firmly seated on the edge of the merry-go-round.

(a) What is the initial angular momentum of the cannonball with respect to the axis passing

through the center of the merry-go-round?

(b) What is the angular velocity of the combination of girl, cannonball, and merry-go-round

immediately after the cannonball was caught?

a) L = m v r =10*15*1.5=225

b) Lfinal = Li = L cannonball = 225 = (0.5*200*1.5^2 + 30*1.5^2 + 10*1.5^2)*w

w= 0.714 rad/s

c) Kelost = Ke initial - Ke final = 0.5*10*15^2 - 0.5*(0.5*200*1.5^2 + 30*1.5^2 + 10*1.5^2)*0.714^2=1044.7 J

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