Three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m, rotate independently around a common axis through their centers. Two of the flywheels rotate in one direction at 8.94 rad/s, but the other one rotates in the opposite direction at 3.42 rad/s.

Required:

Calculate the magnitude of the net angular momentum of the system.

the angular momentum is 1015.52 kg m²/s

Explanation:

given data

mass of each flywheel, m = 65 kg

radius of flywheel, r = 1.47 m

ω1 = 8.94 rad/s

ω2 = - 3.42 rad/s

to find out

magnitude of the net angular momentum

solution

we get here Moment of inertia that is express as

I = 0.5 m r² ... 1

put here value and we get

I = 0.5 * 65 * 1.47 * 1.47

I = 70.23 kg m²

and

now we get here Angular momentum that is express as

L = I * ω ... 2

and Net angular momentum will be

L = 2 * I x ω1 - I * ω2

put here value and we get

L = 2 * 70.23 * 8.94 - 70.23 * 3.42

L = 1015.52 kg m²/s

so

the angular momentum is 1015.52 kg m²/s