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A torque τ is applied to a rigid body with a moment of inertia I. If the torque

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Question: A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)

Options:

  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Correct Answer: It doubles

Exam Year: 2019

Solution: 

According to Newton\'s second law for rotation, τ = Iα. If τ is doubled, α also doubles.

A torque τ is applied to a rigid body with a moment of inertia I. If the torque

Practice Questions

Q1
A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)
  1. It doubles
  2. It halves
  3. It remains the same
  4. It quadruples

Questions & Step-by-Step Solutions

A torque τ is applied to a rigid body with a moment of inertia I. If the torque is doubled, what happens to the angular acceleration? (2019)
  • Step 1: Understand that torque (τ) is a force that causes rotation.
  • Step 2: Know that moment of inertia (I) is a measure of how difficult it is to change the rotation of an object.
  • Step 3: Recall Newton's second law for rotation, which states that torque (τ) equals moment of inertia (I) times angular acceleration (α): τ = Iα.
  • Step 4: If the torque (τ) is doubled, write it as 2τ.
  • Step 5: Substitute 2τ into the equation: 2τ = Iα'. Here, α' is the new angular acceleration.
  • Step 6: Since τ = Iα, we can replace τ in the new equation: 2(Iα) = Iα'.
  • Step 7: Simplify the equation: 2Iα = Iα'.
  • Step 8: Divide both sides by I (assuming I is not zero): 2α = α'.
  • Step 9: This shows that the new angular acceleration (α') is double the original angular acceleration (α).
  • Torque and Angular Acceleration – The relationship between torque (τ), moment of inertia (I), and angular acceleration (α) as described by the equation τ = Iα.
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