If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?
Practice Questions
1 question
Q1
If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?
Both increase
Both decrease
One increases and the other decreases
Remain constant
If angular momentum is conserved, an increase in moment of inertia results in a decrease in angular velocity, and vice versa.
Questions & Step-by-step Solutions
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Q
Q: If the angular momentum of a rotating object is conserved, what can be said about its moment of inertia and angular velocity?
Solution: If angular momentum is conserved, an increase in moment of inertia results in a decrease in angular velocity, and vice versa.
Steps: 4
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.
