A rotating object has a moment of inertia of 3 kg·m² and is spinning with an angular velocity of 4 rad/s. What is its kinetic energy? (2023)

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Q: A rotating object has a moment of inertia of 3 kg·m² and is spinning with an angular velocity of 4 rad/s. What is its kinetic energy? (2023)

Solution: The rotational kinetic energy is given by KE = 0.5 I ω² = 0.5 * 3 * (4)² = 24 J.

Steps: 6

Step 1: Identify the formula for rotational kinetic energy, which is KE = 0.5 * I * ω².
Step 2: Substitute the given moment of inertia (I = 3 kg·m²) into the formula.
Step 3: Substitute the given angular velocity (ω = 4 rad/s) into the formula.
Step 4: Calculate ω², which is (4 rad/s)² = 16 rad²/s².
Step 5: Multiply the moment of inertia (3 kg·m²) by ω² (16 rad²/s²) to get 3 * 16 = 48 kg·m²·rad²/s².
Step 6: Multiply the result by 0.5 to find the kinetic energy: 0.5 * 48 = 24 J.