A rotating object has an angular momentum L. If its moment of inertia is halved
Practice Questions
Q1
A rotating object has an angular momentum L. If its moment of inertia is halved and angular velocity is doubled, what is the new angular momentum? (2022)
L
2L
3L
4L
Questions & Step-by-Step Solutions
A rotating object has an angular momentum L. If its moment of inertia is halved and angular velocity is doubled, what is the new angular momentum? (2022)
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 the changes in the moment of inertia and angular velocity. The moment of inertia (I) is halved, so it becomes I/2. The angular velocity (ω) is doubled, so it becomes 2ω.
Step 3: Substitute the new values into the angular momentum formula. The new angular momentum (L') can be calculated as L' = (I/2)(2ω).
Step 4: Simplify the equation. L' = (1/2)(2ω) = L, which means the new angular momentum is the same as the original angular momentum.
Angular Momentum – Angular momentum (L) is the product of an object's moment of inertia (I) and its angular velocity (ω), 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.
