If the moment of inertia of a body is doubled while keeping the angular velocity

₹0.0

Question: If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)

Options:

Correct Answer: It doubles

Exam Year: 2019

Solution:

Angular momentum L = Iω, so if I is doubled and ω remains constant, L also doubles.

If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)

If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)

Step 1: Understand the formula for angular momentum, which is L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular velocity.
Step 2: Identify that in this scenario, the moment of inertia (I) is doubled. This means if the original moment of inertia is I, the new moment of inertia is 2I.
Step 3: Note that the angular velocity (ω) remains constant, meaning it does not change.
Step 4: Substitute the new moment of inertia into the angular momentum formula: L = (2I)ω.
Step 5: Simplify the equation: L = 2(Iω). This shows that the new angular momentum is twice the original angular momentum.
Step 6: Conclude that if the moment of inertia is doubled while keeping angular velocity constant, the angular momentum also doubles.

Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω) of a rotating body, expressed as L = Iω.
Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation, depending on the mass distribution relative to the axis of rotation.
Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.