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A rotating object has a moment of inertia of 5 kg·m² and is rotating with an ang

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Question: 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)

Options:

  1. 40 J
  2. 20 J
  3. 10 J
  4. 80 J

Correct Answer: 40 J

Exam Year: 2022

Solution: 

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

A rotating object has a moment of inertia of 5 kg·m² and is rotating with an ang

Practice Questions

Q1
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)
  1. 40 J
  2. 20 J
  3. 10 J
  4. 80 J

Questions & Step-by-Step Solutions

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