A rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 4 rad/s. What is its kinetic energy? (2022)

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Q: A rotating object has a moment of inertia of 5 kg·m² and is rotating with an angular velocity of 4 rad/s. What is its kinetic energy? (2022)

Solution: The rotational kinetic energy is given by KE = (1/2)Iω² = (1/2)(5 kg·m²)(4 rad/s)² = 40 J.

Steps: 6

Step 1: Identify the formula for rotational kinetic energy, which is KE = (1/2)Iω².
Step 2: Substitute the given values into the formula. Here, I (moment of inertia) is 5 kg·m² and ω (angular velocity) is 4 rad/s.
Step 3: Calculate ω² (4 rad/s)², which equals 16 rad²/s².
Step 4: Multiply I (5 kg·m²) by ω² (16 rad²/s²) to get 5 kg·m² * 16 rad²/s² = 80 kg·m²·rad²/s².
Step 5: Now, multiply the result by (1/2). So, (1/2) * 80 kg·m²·rad²/s² = 40 J.
Step 6: The final answer is the kinetic energy, which is 40 Joules.