Final answer:
The angular momentum of a solid uniform sphere can be calculated using the formula L = Iω, with the moment of inertia I for a solid sphere given by I = (2/5)mr².
Step-by-step explanation:
To calculate the angular momentum of a solid uniform sphere with a radius of 0.125 m and a mass of 12.0 kg rotating at 6.40 rad/s about an axis through its center, we use the formula for angular momentum, L = I·ω, where I is the moment of inertia and ω is the angular velocity.
To find the moment of inertia I for a solid sphere, we use the formula I = (2/5)mr², where m is the mass of the sphere and r is its radius. Substituting the given values, we get I = (2/5)(12.0 kg)(0.125 m)².
After calculating I, we multiply it by the angular velocity ω to find the angular momentum. Thus, angular momentum L = (2/5)(12.0 kg)(0.125 m)²(6.40 rad/s).
The calculated result gives us the sphere's angular momentum about the axis through its center.