A rotating object has an angular momentum of L. If its moment of inertia is doub
Practice Questions
Q1
A rotating object has an angular momentum of L. If its moment of inertia is doubled while keeping the angular velocity constant, what will happen to its angular momentum?
It doubles
It halves
It remains the same
It becomes zero
Questions & Step-by-Step Solutions
A rotating object has an angular momentum of L. If its moment of inertia is doubled while keeping the angular velocity constant, what will happen to its angular momentum?
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 that in this scenario, the moment of inertia (I) is doubled.
Step 3: Note that the angular velocity (ω) remains constant.
Step 4: Substitute the new moment of inertia into the formula: if I is doubled, we can write it as L' = (2I)ω.
Step 5: Since ω is constant, we can see that L' = 2Iω, which means the new angular momentum would be double the original if ω were not constant.
Step 6: However, since we are keeping ω constant, we realize that the angular momentum L does not change because the relationship L = Iω holds true.
Step 7: Conclude that even though I is doubled, the angular momentum L remains the same because the increase in I is offset by the constant ω.
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.
Conservation of Angular Momentum – In a closed system with no external torques, angular momentum is conserved, meaning it remains constant unless acted upon by an external force.
