If the radius of a disk is doubled while keeping its mass constant, how does its

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Question: If the radius of a disk is doubled while keeping its mass constant, how does its moment of inertia change?

Options:

Correct Answer: Increases by a factor of 4

Solution:

The moment of inertia of a disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.

If the radius of a disk is doubled while keeping its mass constant, how does its moment of inertia change?

If the radius of a disk is doubled while keeping its mass constant, how does its moment of inertia change?

Step 1: Understand the formula for the moment of inertia of a disk, which is I = 1/2 MR^2, where M is mass and R is the radius.
Step 2: Note that we are keeping the mass (M) constant while changing the radius (R).
Step 3: If the radius is doubled, we replace R with 2R in the formula.
Step 4: Substitute 2R into the moment of inertia formula: I = 1/2 M(2R)^2.
Step 5: Calculate (2R)^2, which equals 4R^2.
Step 6: Now the formula looks like this: I = 1/2 M(4R^2).
Step 7: Simplify the equation: I = 2MR^2.
Step 8: Compare the new moment of inertia (2MR^2) with the original (1/2 MR^2).
Step 9: Notice that 2MR^2 is 4 times the original moment of inertia (1/2 MR^2).

Moment of Inertia – The moment of inertia quantifies how mass is distributed relative to an axis of rotation, affecting rotational motion.
Effect of Radius on Moment of Inertia – The moment of inertia increases with the square of the radius, meaning if the radius is doubled, the moment of inertia increases by a factor of four.