A rotating object has an angular momentum of L. If its angular velocity is doubl
Practice Questions
Q1
A rotating object has an angular momentum of L. If its angular velocity is doubled and its moment of inertia remains constant, what will be 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 angular velocity is doubled and its moment of inertia remains constant, what will be 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: Note that in this problem, the moment of inertia (I) remains constant.
Step 3: Recognize that if the angular velocity (ω) is doubled, it becomes 2ω.
Step 4: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
Step 5: Simplify the equation: L = 2Iω.
Step 6: Since the original angular momentum is L = Iω, we can express the new angular momentum as L' = 2L.
Step 7: Therefore, if we double the angular velocity, the new angular momentum becomes 4L.
Angular Momentum – Angular momentum (L) is the product of an object's moment of inertia (I) and its angular velocity (ω).
Moment of Inertia – Moment of inertia (I) is a measure of an object's resistance to changes in its rotation.
Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.
