A sphere of uniform density, with mass 18 kg and radius 0.8 m, is located at the origin and rotates around an axis parallel with the axis. If you stand somewhere on the axis and look toward the origin at the sphere, the sphere spins counterclockwise. One complete revolution takes 0.7 s. What is the rotational angular momentum of the sphere? What is the rotational kinetic energy of the sphere? (Express your answer for rotational angular momentum in vector form.)

Explanation:

Given that,

Mass of sphere M = 18kg

Radius R = 0.8m

Angular revolution is

It completes 1 revolution in 0.7sec

θ = 1 rev, t = 0.1sec

1 rev = 2πrad

Then, ω = θ / t

ω = 2π/0.7 = 8.98 rad/s

A. Angular momentum is given as

L = Iω

I is moment of inertial

Moment of inertial of a sphere is given as

I = 2/5 • MR²

I = 2/5 × 18 × 0.8²

I = 4.61 kgm²

Then,

L = Iω

L = 4.61 × 8.98

L = 41.38 kgm²/s

Rotational kinetic energy

K.E = ½Iω²

K.E = ½ × 4.61 × 8.98²

K.E = 185.88 J

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