Question

Calculate kinetic energy of a solid uniform sphere with a radius of 0.115 m and a mass of 16.0 kg if it is rotating at 5.75 rad/s about an axis through its center.

Answer 1

The kinetic energy of the rotating solid uniform sphere is 13.296 J

Step-by-step explanation:

To calculate the kinetic energy of a rotating solid uniform sphere, we use the formula:

KErot = (1/2) * I * ω²

Where:

• KErot is the rotational kinetic energy
• I is the moment of inertia of the sphere
• ω is the angular velocity of the sphere

The moment of inertia of a solid uniform sphere is given by:

I = (2/5) * m * r²

Where:

• m is the mass of the sphere
• r is the radius of the sphere

Substituting the given values into these formulas:

I = (2/5) * 16.0 kg * (0.115 m)² = 0.66208 kg·m²

ω = 5.75 rad/s

Now, we can calculate the kinetic energy:

KErot = (1/2) * 0.66208 kg·m² * (5.75 rad/s)² = 13.296 J