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A rotating object has a moment of inertia of 3 kg·m² and is rotating with an ang

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Question: A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?

Options:

  1. 15 J
  2. 30 J
  3. 50 J
  4. 100 J

Correct Answer: 30 J

Solution: 

Rotational kinetic energy K = (1/2)Iω² = (1/2)(3 kg·m²)(10 rad/s)² = 150 J.

A rotating object has a moment of inertia of 3 kg·m² and is rotating with an ang

Practice Questions

Q1
A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?
  1. 15 J
  2. 30 J
  3. 50 J
  4. 100 J

Questions & Step-by-Step Solutions

A rotating object has a moment of inertia of 3 kg·m² and is rotating with an angular velocity of 10 rad/s. What is its rotational kinetic energy?
Correct Answer: 150 J
  • Step 1: Identify the formula for rotational kinetic energy, which is K = (1/2)Iω².
  • Step 2: Identify the moment of inertia (I) given in the problem, which is 3 kg·m².
  • Step 3: Identify the angular velocity (ω) given in the problem, which is 10 rad/s.
  • Step 4: Substitute the values into the formula: K = (1/2)(3 kg·m²)(10 rad/s)².
  • Step 5: Calculate (10 rad/s)², which equals 100 rad²/s².
  • Step 6: Multiply 3 kg·m² by 100 rad²/s² to get 300 kg·m²·rad²/s².
  • Step 7: Multiply 300 kg·m²·rad²/s² by (1/2) to get 150 J.
  • Step 8: Conclude that the rotational kinetic energy is 150 J.
  • Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula K = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
  • Moment of Inertia – A measure of an object's resistance to changes in its rotation, dependent on the mass distribution relative to the axis of rotation.
  • Angular Velocity – The rate of rotation of an object, measured in radians per second.
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