Question

A satellite is rotating once per minute. It has an moment of inertia of 10,000kg⋅m2. An astronaut extends the satellite's solar panels, increasing its moment of inertia to 30,000kg⋅m2. How quickly is the satellite now rotating?

Answer 1

Answer:3 minutes

Explanation:

Given

initial moment of Inertia $I_1=10,000 kg.m^2$

Time Period $T_1=1 minute$

Final Moment of Inertia $I_2=30,000 kg.m^2$

Let T be the Time Period Of revolution

Conserving Angular Momentum

$I_1\omega _1=I_2\omega _2$

$I_1(\frac{2\pi }{T_1})=I_2(\frac{2\pi }{T})$

$\frac{I_1}{T_1}=\frac{I_2}{T}$

$\frac{10,000}{1}=\frac{30,000}{T}$

$T=\frac{30,000}{10,000}=3 minutes$

i.e. 1 rotation in 3 minutes

Answer 2

Increasing the moment of inertia of the satellite makes it to complete a revolution in 3 mins hence slower

What is moment of Inertia of a rotating body?

moment of inertia, I is the measure of distibution of the mass of the body along the axis of rotatiton.

I = angular momentum, L  / angular velocity, ω

L = I * ω

L1 = L2

I1 * ω1 = I2 * ω2 for an isolated system

10000 * 1 = 30000 * ω2

ω2 = 10000 / 30000

ω2 = 0.333rpm

initially the satellite is making one revolution per minute

ω1 = 1 revolution in 1 min

ω2 = 0.33 revolution in 1 min = 1 revolution in 3 min

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