Final answer:
Rotational kinetic energy of a solid uniform sphere is calculated using the formula KErot = 1/2 I ω², where I is the moment of inertia and ω is the angular velocity. For a solid sphere, I = 2/5 mr². The calculated kinetic energy for the given sphere is approximately 9.5 joules.
Step-by-step explanation:
Rotational Kinetic Energy of a Sphere
To calculate the rotational kinetic energy (KErot) of a solid uniform sphere, you can use the formula:
KErot = ½ I ω²
Where I is the moment of inertia of the sphere and ω (omega) is the angular velocity. For a solid sphere, the moment of inertia is calculated using the formula I = ¾ mr², where m is the mass of the sphere, and r is the radius.
Now, let's plug in the given values: The mass (m) is 14.5 kg, the radius (r) is 0.145 m, and the angular velocity (ω) is 6.40 rad/s.
I = ¾ (14.5 kg) (0.145 m)² = 0.463625 kg·m²
Next, we calculate KErot:
KErot = ½ (0.463625 kg·m²) (6.40 rad/s)² ≈ 9.5 J
Therefore, the rotational kinetic energy of the sphere is approximately 9.5 joules.