If the angular momentum of a rotating object is conserved, what can be said abou

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Question: If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?

Options:

Correct Answer: One increases and the other decreases

Solution:

If angular momentum is conserved, an increase in moment of inertia results in a decrease in angular velocity, and vice versa.

If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?

If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?

Step 1: Understand what angular momentum is. Angular momentum (L) is a measure of how much motion an object has while it is rotating. It is calculated using the formula L = I * ω, where I is the moment of inertia and ω is the angular velocity.
Step 2: Know what is meant by conservation of angular momentum. When we say angular momentum is conserved, it means that the total angular momentum of the system remains constant over time, as long as no external forces are acting on it.
Step 3: Recognize the relationship between moment of inertia and angular velocity. If the moment of inertia (I) increases, the angular velocity (ω) must decrease to keep the angular momentum (L) the same, and vice versa.
Step 4: Apply the concept. If an object is rotating and its moment of inertia increases (for example, if it spreads out its mass), its angular velocity must decrease to maintain the same angular momentum. If the moment of inertia decreases, the angular velocity must increase.

Angular Momentum Conservation – Angular momentum (L) is conserved in a closed system, meaning L = I * ω remains constant, where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia and Angular Velocity Relationship – The relationship between moment of inertia and angular velocity is inversely proportional when angular momentum is conserved: if I increases, ω decreases, and vice versa.