# Calculate the rotational kinetic energy of the Sun in joules

#### kt102188

1. Homework Statement

Assume the Sun is a uniform, rigid sphere (it is spherically shaped but actually is not of uniform density nor a rigid body). The Sun rotates once every 27 days.
(a) Calculate the rotational kinetic energy of the Sun in joules.

(b) The luminosity (power output) of the Sun is 3.826 x 1026 W, a rather powerful light bulb! For how many years could the Sun shine at its present luminosity if it were radiating away its rotational kinetic energy?

[The energy source of the Sun is not the rotational kinetic energy but rather the nuclear fusion of hydrogen nuclei, creating helium.]

2. Homework Equations

T=2(Pi)r/v
KErot=0.5Icenter of mass*angular velocity2
Icenter of mass= 2/5Mr2 for a solid sphere about any diameter
Angular Velocity=

3. The Attempt at a Solution
I'm having trouble with so few numbers.
I googled the mass of the sun and got 1.98892e30 kilograms and the radius of the sun = 695 500 000 meters

T=2(Pi)r/v
v/r= 2pi/T T=27days=2332800s
v/r=2.6934e-6

KErot=(1/2)(2/5)mr2(v/r)2
KE=(.2)M of Sun (r of sun)2 (2.6934e-6)
KE=.2(1.98891e30)(6.95e8)2(2.6934e-6)2
KE=1.39385e36
I double checked my math, and this is the right answer! :)

I have no idea how to do part B though.

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"Calculate the rotational kinetic energy of the Sun in joules"

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