Amerry-go-round is a common piece of playground equipment. a 3.0-m-diameter merry-go-round, which can be modeled as a disk with a mass of 300 kg , is spinning at 25 rpm. john runs tangent to the merry-go-round at 5.8 m/s, in the same direction that it is turning, and jumps onto the outer edge. john's mass is 30 kg.

w2 = 2.83 rad/s  

Explanation:

The moment of inertia of the merry-go-round is

I = (1/2) M R^2

I = 1/2 * 300 kg * 1.5 m^2

I = 337.5 kg*m^2

The initial angular velocity of the merry-go-round is

w1 = 25 rpm *2*pi /60

w1 = 2.6 rad/s

The angular momentum conservation equation is:

I*w1 + m*R*v = (I + mR^2)*w2

where m is John's mass.

337.5*2.6 + 30*1.5*2.6 = (337.5 + 30*(1.5)^2)

887.5 + 261 = (337.5 + 67.5)*w2

w2 = 2.83 rad/s

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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