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A rotating object has an angular velocity of 30 rad/s and a moment of inertia of
A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?
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Q1
A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?
135 J
450 J
270 J
90 J
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Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(30 rad/s)² = 450 J.
Questions & Step-by-step Solutions
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Q
Q: A rotating object has an angular velocity of 30 rad/s and a moment of inertia of 3 kg·m². What is its rotational kinetic energy?
Solution:
Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(30 rad/s)² = 450 J.
Steps: 7
Show Steps
Step 1: Identify the formula for rotational kinetic energy, which is K = (1/2)Iω².
Step 2: Identify the values given in the problem: moment of inertia (I) = 3 kg·m² and angular velocity (ω) = 30 rad/s.
Step 3: Substitute the values into the formula: K = (1/2)(3 kg·m²)(30 rad/s)².
Step 4: Calculate (30 rad/s)², which is 900 rad²/s².
Step 5: Multiply 3 kg·m² by 900 rad²/s² to get 2700 kg·m²·rad²/s².
Step 6: Multiply 2700 by (1/2) to get 1350 kg·m²·rad²/s².
Step 7: The final result is K = 1350 J, which is the rotational kinetic energy.
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