2. Merry-go-round (8 points). While merry-go-rounds aré seeh as dangerous playgr

Question

2. Merry-go-round (8 points). While merry-go-rounds aré seeh as dangerous playground equipment by some, by others (u deal of physics. At a nearby playground, you come upon an empty merry-go- round (see below) that is rotating about its central (assumed to be frictionless) axis at 3 rad/s. Despite the bars sticking out of the merry-go- round (drawn as white rectangles), we will treat it as a uniform cylinder with a diameter of 1.8m. The initial rotational inertia of the merry-go-round is 200 kg m2 s) they are a source of a great Mud 60 kg U M Mmeryd-1.8 m M 60 kg om 3 rad/s pus . ? a. While you watch, three kids of equal mass (60 kg) who were standing by the side of the merry-go-round jump in the radial direction onto the merry-go-round (as shown above). The children can be treated as point masses at a distance of 0.9 m from the center of the merry-go-round. What is the new rotational velacity of the meryyao-raund?

Explanation / Answer

a)

new rotational inertia = I + 3*m*R^2

R = radius = D?2 = 1.8/2 = 0.9 m

m = 60 kg

I = 200

new rotational inertia Inew = 200+(3*60*0.9^2) = 345.8 kgm^2

from angular momentum conservation

Lnew = Lold

Inew*wnew = Iold*wold

345.8*wnew = 200*3

wnew = 1.735 rad/s

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b)

centrifugal force = frictional force

m*R*w^2 = f

f = 60*0.9*9^2 = 4374 N

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