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A flywheel has a moment of inertia I and is rotating with an angular velocity ω.

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Question: A flywheel has a moment of inertia I and is rotating with an angular velocity ω. If a torque τ is applied to it, what is the angular acceleration α?

Options:

  1. τ/I
  2. I/τ
  3. Iω/τ
  4. τω/I

Correct Answer: τ/I

Solution: 

From Newton\'s second law for rotation, τ = Iα, thus α = τ/I.

A flywheel has a moment of inertia I and is rotating with an angular velocity ω.

Practice Questions

Q1
A flywheel has a moment of inertia I and is rotating with an angular velocity ω. If a torque τ is applied to it, what is the angular acceleration α?
  1. τ/I
  2. I/τ
  3. Iω/τ
  4. τω/I

Questions & Step-by-Step Solutions

A flywheel has a moment of inertia I and is rotating with an angular velocity ω. If a torque τ is applied to it, what is the angular acceleration α?
  • Step 1: Understand that a flywheel is an object that can rotate.
  • Step 2: Know that 'moment of inertia' (I) is a measure of how difficult it is to change the rotation of the flywheel.
  • Step 3: Recognize that 'angular velocity' (ω) is how fast the flywheel is spinning.
  • Step 4: Learn that 'torque' (τ) is a force that causes the flywheel to start spinning faster or slower.
  • Step 5: Remember Newton's second law for rotation, which states that torque (τ) is equal to moment of inertia (I) times angular acceleration (α).
  • Step 6: Write the equation: τ = Iα.
  • Step 7: To find angular acceleration (α), rearrange the equation to solve for α: α = τ/I.
  • Step 8: Now you can calculate the angular acceleration if you know the torque and moment of inertia.
  • Moment of Inertia – The resistance of a body to changes in its rotational motion, dependent on mass distribution.
  • Torque – A measure of the force that can cause an object to rotate about an axis.
  • Angular Acceleration – The rate of change of angular velocity, indicating how quickly an object is speeding up or slowing down its rotation.
  • Newton's Second Law for Rotation – The relationship between torque, moment of inertia, and angular acceleration, expressed as τ = Iα.
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