A rotating object has an angular momentum of L. If its moment of inertia is halv
Practice Questions
Q1
A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
L
2L
4L
L/2
Questions & Step-by-Step Solutions
A rotating object has an angular momentum of L. If its moment of inertia is halved and the angular velocity is doubled, what is the new angular momentum?
Step 1: Understand that angular momentum (L) is calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
Step 2: Identify the initial angular momentum, which is given as L.
Step 3: Note that the moment of inertia (I) is halved, so the new moment of inertia (I') is I' = 1/2 I.
Step 4: Recognize that the angular velocity (ω) is doubled, so the new angular velocity (ω') is ω' = 2ω.
Step 5: Substitute the new values into the angular momentum formula: L' = I'ω' = (1/2 I)(2ω).
Step 6: Simplify the equation: L' = (1/2)(2)(Iω) = Iω.
Step 7: Since Iω is the original angular momentum L, we find that L' = L.
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.
Conservation of Angular Momentum – In a closed system, the total angular momentum remains constant if no external torques act on it.
