1. A 5g bug is sitting on the edge of a horizontal disk. The disk has a mass of

Question

1. A 5g bug is sitting on the edge of a horizontal disk. The disk has a mass of 10kg and a diameter of .5m. Together, the bug and disk are rotating at 100rpm.

a. What is the total moment of inertia of the bug and disk together? (Hint: moments of inertia are additive!)

b. The bug decides to start walking towards the center of the disk, while it is rotating. What is the angular velocity of the system by the time the bug makes it half way to the center? (Hint: use angular momentum conservation! You first have to find out what the new moment of inertia is when the bug is halfway to the center.)

Explanation / Answer

here,

mass of bug , m1 = 5 g = 0.005 kg

mass of disk , m2 = 10 kg

diameter , d = 0.5 m

radius , r = 0.25 m

a)

the total moment of inertia of the bug and disk together , I = m1 * r^2 + 0.5 * m2 * r^2

I = (0.005 + 0.5 * 10 ) * 0.25^2 kg.m^2

I = 0.3128 kg.m^2

b)

initial angular speed , w0 = 100 rpm

the final moment of inertia , I' = m1 * (r/2)^2 + 0.5 * m2 * r^2

I' = (0.005 * ( 0.25 /2)^2 + 0.5 * 10 * 0.25^2 kg.m^2

I' = 0.31257 kg.m^2

let the final speed be w

using conservation of angular momentum

I * w0 = I' * w

0.3128 * 100 = 0.31257 * w

w = 100.08 rpm

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