Question

calculate the angular momentum of a solid uniform sphere with a radius of 0.135 m and a mass of 16.0 kg if it is rotating at 5.85 rad/s about an axis through its center.

Answer 1

The angular momentum of the rotating solid uniform sphere with a radius of 0.135 m, a mass of 16.0 kg, and an angular velocity of 5.85 rad/s is 0.8552 kg·m^2/s.

Step-by-step explanation:

To calculate the angular momentum (L) of a rotating solid uniform sphere, we use the formula L = I×ω, where I is the moment of inertia and ω is the angular velocity. For a solid sphere rotating about an axis through its center, the moment of inertia is I = 2/5 × m × r^2, where m is the mass of the sphere and r is the radius. Substituting the provided values, we have:

I = 2/5 × 16.0 kg × (0.135 m)^2 = 0.14616 kg·m^2

Now, utilizing the angular velocity given:

ω = 5.85 rad/s

The angular momentum of the sphere is:

L = I × ω = 0.14616 kg·m^2 × 5.85 rad/s = 0.8552 kg·m^2/s