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If the moment of inertia of a body is doubled, what will be the effect on its an

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Question: If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?

Options:

  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases by a factor of four

Correct Answer: Halves

Solution: 

Angular acceleration α = τ/I. If I is doubled and τ remains constant, α is halved.

If the moment of inertia of a body is doubled, what will be the effect on its an

Practice Questions

Q1
If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
  1. Doubles
  2. Halves
  3. Remains the same
  4. Increases by a factor of four

Questions & Step-by-Step Solutions

If the moment of inertia of a body is doubled, what will be the effect on its angular acceleration if the torque applied remains constant?
  • Step 1: Understand the formula for angular acceleration, which is α = τ/I, where α is angular acceleration, τ is torque, and I is moment of inertia.
  • Step 2: Identify that if the moment of inertia (I) is doubled, it becomes 2I.
  • Step 3: Keep the torque (τ) constant in the equation.
  • Step 4: Substitute the new moment of inertia into the formula: α = τ/(2I).
  • Step 5: Compare the new angular acceleration to the original: the new angular acceleration is half of the original angular acceleration.
  • Step 6: Conclude that if the moment of inertia is doubled and torque remains constant, the angular acceleration is halved.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
  • Torque – Torque is the rotational equivalent of linear force, representing the tendency of a force to rotate an object about an axis.
  • Angular Acceleration – Angular acceleration is the rate of change of angular velocity, influenced by the applied torque and the moment of inertia.
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