A disk of gas and dust forming in our solar system begins with a radius of 1 mil

Question

A disk of gas and dust forming in our solar system begins with a radius of 1 million km and a tangential velocity of v=100m/s. Over time it will shrink to a radius of 10000km. Use conservation of angular momentum to determine the angular velocity of the disk after it shrinks. L disk=1/2mr^2
A disk of gas and dust forming in our solar system begins with a radius of 1 million km and a tangential velocity of v=100m/s. Over time it will shrink to a radius of 10000km. Use conservation of angular momentum to determine the angular velocity of the disk after it shrinks. L disk=1/2mr^2

Explanation / Answer

From law of conservation of angular momentum

angular momentum Before shrinks = angular momentum after shrinks

angular momentum L = I*w

I1*w1 = I2*w2

I1 = 0.5*m*r1^2

w1 = V/r1 = 100/10^9 = 10^-7 rad/s

I2 = 0.5*m*r2^2

w2= ?

I1*w1 = I2*w2

0.5*m*r1^2*w1 = 0.5*m*r2^2*w2

r1^2*w1 = r2^2*w2

w2 = (r1/r2)^2*w1 = (10^9/10^7)^2*10^-7 =10^-3 rad/s

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