A rotating object has an angular momentum L. If the moment of inertia of the obj
Practice Questions
Q1
A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the angular momentum?
It doubles
It halves
It remains the same
It quadruples
Questions & Step-by-Step Solutions
A rotating object has an angular momentum L. If the moment of inertia of the object is doubled while keeping the angular velocity constant, what happens to the 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 that in this scenario, the moment of inertia (I) is being doubled. This means if the original moment of inertia is I, the new moment of inertia will be 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: Compare the new angular momentum (L) with the original angular momentum. Since L = Iω originally, the new angular momentum becomes L = 2(Iω).
Step 6: Conclude that since the new angular momentum is 2 times the original angular momentum, the angular momentum doubles.
Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω) of an object, 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.
