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A disk rotates about its axis with an angular velocity of Ο‰. If its radius is do

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Question: A disk rotates about its axis with an angular velocity of Ο‰. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?

Options:

  1. 2I
  2. 4I
  3. I
  4. I/2

Correct Answer: 4I

Solution: 

The moment of inertia of a disk is I = (1/2)MR^2. If the radius is doubled, the new moment of inertia becomes I\' = (1/2)M(2R)^2 = 4I.

A disk rotates about its axis with an angular velocity of Ο‰. If its radius is do

Practice Questions

Q1
A disk rotates about its axis with an angular velocity of Ο‰. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?
  1. 2I
  2. 4I
  3. I
  4. I/2

Questions & Step-by-Step Solutions

A disk rotates about its axis with an angular velocity of Ο‰. If its radius is doubled while keeping the mass constant, what will be the new moment of inertia?
  • Step 1: Understand the formula for the moment of inertia of a disk, which is I = (1/2)MR^2, where M is the mass and R is the radius.
  • Step 2: Identify that the radius of the disk is being doubled. This means the new radius will be 2R.
  • Step 3: Substitute the new radius into the moment of inertia formula. The new moment of inertia I' will be I' = (1/2)M(2R)^2.
  • Step 4: Calculate (2R)^2, which equals 4R^2.
  • Step 5: Substitute 4R^2 back into the formula: I' = (1/2)M(4R^2).
  • Step 6: Simplify the equation: I' = 4 * (1/2)MR^2, which means I' = 4I, where I is the original moment of inertia.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, calculated as I = (1/2)MR^2 for a disk.
  • Angular Velocity – Angular velocity (Ο‰) describes how fast an object rotates around an axis, but it is not directly affected by changes in radius when mass is constant.
  • Effect of Radius on Moment of Inertia – Doubling the radius of a disk increases its moment of inertia by a factor of four, as it is proportional to the square of the radius.
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