1)A boulder with a radius of 10 m and mass of 1000 kg starts from rest and rolls

Question

1)A boulder with a radius of 10 m and mass of 1000 kg starts from rest and rolls down a hill of Height h = 100m. Use conservation of energy to determine the velocity of the boulder when it Hits the bottom of the hill, I sphere = 2/5mr^2 2) A disk of gas and dust forming our solar system begins with a radius of 1 million km and a tangential velocity of v=100 m/s. Over time it will shrink to a radius of 10000 km. Use conservation of angular momentum to determine the angular velocity of the disk after it shrink I disk = 1/2mr^2

Explanation / Answer

from conservation of energy

mgh = 1/2 mv^2 + 1/2 IW^2

mgh = (1/2)mv^2 +(1/2)(2/5)mr^2(v/r)^2

mgh = (7/10)mv^2

v^2 = 10gh/7 = 10*9.8*100/7

v = 37.4 m/s

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