A rotating body has an angular momentum L. If its moment of inertia is doubled a
Practice Questions
Q1
A rotating body has an angular momentum L. If its moment of inertia is doubled and angular velocity is halved, what will be the new angular momentum? (2021)
L/2
L
2L
4L
Questions & Step-by-Step Solutions
A rotating body has an angular momentum L. If its moment of inertia is doubled and angular velocity is halved, what will be the new angular momentum? (2021)
Step 1: Understand that angular momentum (L) is calculated using the formula L = I * ω, where I is the moment of inertia and ω is the angular velocity.
Step 2: Identify the initial values: Let the initial moment of inertia be I and the initial angular velocity be ω. Therefore, the initial angular momentum is L = I * ω.
Step 3: Note that the moment of inertia is doubled, so the new moment of inertia (I') is 2I.
Step 4: Note that the angular velocity is halved, so the new angular velocity (ω') is ω/2.
Step 5: Calculate the new angular momentum (L') using the new values: L' = I' * ω' = (2I) * (ω/2).
Step 6: Simplify the equation: L' = 2I * (ω/2) = I * ω.
Step 7: Recognize that I * ω is the original angular momentum L, so L' = L.
Angular Momentum – Angular momentum (L) is the product of a body'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.
