Question

Two identical spheres with m=3 kg each are rigidly attached to the rotating light rigid structure. The velocity of the spheres is v=2 m/s. Determine the angular momentum about the axis of rotation.

Answer 1

The angular momentum of each sphere is 24 kg·m²/s, and the total angular momentum of the system is 48 kg·m²/s.

Step-by-step explanation:

To determine the angular momentum of the two identical spheres about the axis of rotation, we can use the formula:

Angular Momentum (L) = Moment of Inertia (I) x Angular Velocity (ω)

Since the spheres are identical and rigidly attached to the rotating structure, they have the same moment of inertia. The moment of inertia for a sphere of mass m and radius r is given by: I = (2/5)mr^2

Therefore, the angular momentum of each sphere is: L = (2/5)(3 kg)(2 m/s)(2 m)^2 = 24 kg·m²/s

Since the two spheres are identical and have the same angular momentum, the total angular momentum of the system is: Total Angular Momentum = 2 x 24 kg·m²/s = 48 kg·m²/s