# Physics Help: Their rotation kinetic energies compare as.....?

The mass of the sun is about 270,000 times that of earth, and its radius is about 100 times that of earth. The rotation period of the sun is about 30 times that of the earth. Treat both the earth and sun as solid spheres. Their rotation kinetic energies compare as....

a) K(sun) ~ 81,000 K(earth)

b) K(sun) ~ 900,000 K(earth)

c) K(sun) ~ 3 x 10^6 (earth)

d) K(sun) ~ 30,000 K(earth)

### 1 Answer

- billrussell42Lv 72 months ago
E = ½Iω² = E = ½(2/5)MR²ω² = (1/5)MR²ω²

mass scales linearly, so E would be x 270000

radius scales as the square, so E would be x 100²

angular velocity scales as the square, so E would be x 30²

altogether, we have 270000 x 10000 x 900 = 243e10

none of your answers are even close.

Angular kinetic energy E in Joules

E = ½Iω²

ω is angular velocity in radians/sec

I = moment of inertia in kg•m²

I = cMR²

M is mass (kg), R is radius (meters)

c = 1 for a ring or hollow cylinder

c = 2/5 solid sphere around a diameter

c = 7/5 solid sphere around a tangent

c = ⅔ hollow sphere around a diameter