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

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Question: 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)

Options:

  1. 12 J
  2. 24 J
  3. 48 J
  4. 6 J

Correct Answer: 24 J

Exam Year: 2023

Solution: 

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

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

Practice Questions

Q1
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)
  1. 12 J
  2. 24 J
  3. 48 J
  4. 6 J

Questions & Step-by-Step Solutions

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)
  • 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.
  • Rotational Kinetic Energy – The energy possessed by a rotating object, calculated using the formula KE = 0.5 I ω², 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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