A rotating wheel has an angular momentum of L. If the wheel's angular velocity i

A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what will be the new angular momentum?

A rotating wheel has an angular momentum of L. If the wheel's angular velocity is doubled, what will be the new angular momentum?

Step 1: Understand that angular momentum (L) is related to angular velocity (ω). The formula for angular momentum is L = I * ω, where I is the moment of inertia.
Step 2: Recognize that if the angular velocity (ω) is doubled, we can express this as ω' = 2ω, where ω' is the new angular velocity.
Step 3: Substitute the new angular velocity into the angular momentum formula: L' = I * ω' = I * (2ω).
Step 4: Simplify the equation: L' = 2 * (I * ω) = 2L, which shows that angular momentum is now twice the original value.
Step 5: However, since angular momentum is proportional to the square of the angular velocity, if we double the angular velocity, the angular momentum actually becomes 4 times the original: L' = 4L.

Angular Momentum – Angular momentum (L) is a vector quantity that represents the rotational inertia and rotational velocity of an object. It is calculated as L = Iω, where I is the moment of inertia and ω is the angular velocity.
Proportionality of Angular Momentum and Angular Velocity – Angular momentum is directly proportional to angular velocity. If angular velocity is doubled, angular momentum also doubles, assuming the moment of inertia remains constant.