A rotating wheel has an angular momentum of L. If its angular velocity is double

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

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

Step 1: Understand that angular momentum (L) is calculated using the formula L = Iω, where I is the moment of inertia and ω is the angular velocity.
Step 2: Identify that if the angular velocity (ω) is doubled, it becomes 2ω.
Step 3: Substitute the new angular velocity into the angular momentum formula: L = I(2ω).
Step 4: Rewrite the equation: L = 2Iω.
Step 5: Notice that the original angular momentum was L = Iω, so we can replace Iω with L in the new equation: L = 2L.
Step 6: Realize that the moment of inertia (I) does not change, so we can also express the new angular momentum as L = 4L, since we have doubled the angular velocity.

Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and the angular velocity (ω) of a rotating object.
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.
Angular Velocity – Angular velocity (ω) is the rate of rotation of an object, typically measured in radians per second.