If the moment of inertia of a body is doubled, what happens to its rotational ki

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Question: If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?

Options:

Correct Answer: Doubles

Solution:

Rotational kinetic energy is given by KE = 1/2 I ω^2. If I is doubled and ω remains constant, KE also doubles.

If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?

If the moment of inertia of a body is doubled, what happens to its rotational kinetic energy if the angular velocity remains constant?

Step 1: Understand the formula for rotational kinetic energy, which is KE = 1/2 I ω^2.
Step 2: Identify the variables in the formula: I is the moment of inertia and ω is the angular velocity.
Step 3: Note that in this scenario, the moment of inertia (I) is doubled, so we can write it as 2I.
Step 4: Since the angular velocity (ω) remains constant, we can substitute 2I into the formula: KE = 1/2 (2I) ω^2.
Step 5: Simplify the equation: KE = (1/2 * 2) I ω^2, which simplifies to KE = I ω^2.
Step 6: Compare the new kinetic energy (KE = I ω^2) with the original kinetic energy (KE = 1/2 I ω^2).
Step 7: Since the new kinetic energy is twice the original kinetic energy, we conclude that if the moment of inertia is doubled, the rotational kinetic energy also doubles.

Rotational Kinetic Energy – The formula for rotational kinetic energy is KE = 1/2 I ω^2, where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, depending on its mass distribution.
Angular Velocity – Angular velocity is the rate of rotation of an object, typically measured in radians per second.