If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)
Practice Questions
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Q1
If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)
It doubles
It remains the same
It halves
It quadruples
Angular momentum L = Iω, so if I is doubled and ω remains constant, L also doubles.
Questions & Step-by-step Solutions
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Q
Q: If the moment of inertia of a body is doubled while keeping the angular velocity constant, what happens to its angular momentum? (2019)
Solution: Angular momentum L = Iω, so if I is doubled and ω remains constant, L also doubles.
Steps: 6
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. This means if the original moment of inertia is I, the new moment of inertia is 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: Simplify the equation: L = 2(Iω). This shows that the new angular momentum is twice the original angular momentum.
Step 6: Conclude that if the moment of inertia is doubled while keeping angular velocity constant, the angular momentum also doubles.
