If the radius of a rotating object is halved while keeping the mass constant, ho

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

Options:

Correct Answer: It reduces to one-fourth

Solution:

Moment of inertia I is proportional to the square of the radius, so halving the radius reduces I to one-fourth.

If the radius of a rotating object is halved while keeping the mass constant, how does its moment of inertia change?

If the radius of a rotating object is halved while keeping the mass constant, how does its moment of inertia change?

Step 1: Understand what moment of inertia (I) is. It measures how difficult it is to change the rotation of an object.
Step 2: Know the formula for moment of inertia for a solid object, which is I = k * m * r^2, where k is a constant, m is mass, and r is radius.
Step 3: Recognize that if the radius (r) is halved, we can express this as r' = r / 2.
Step 4: Substitute the new radius into the moment of inertia formula: I' = k * m * (r / 2)^2.
Step 5: Simplify the equation: I' = k * m * (r^2 / 4) = (1/4) * (k * m * r^2).
Step 6: Conclude that the new moment of inertia (I') is one-fourth of the original moment of inertia (I).

Moment of Inertia – The moment of inertia (I) of an object is a measure of its resistance to angular acceleration, which depends on the mass distribution relative to the axis of rotation.
Proportionality to Radius – The moment of inertia is proportional to the square of the radius (I ∝ r²), meaning that changes in radius have a quadratic effect on I.