A disk of radius R and mass M is rotating about its axis with an angular velocit

A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum?

A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum?

Step 1: Understand that angular momentum (L) is a measure of how much motion an object has while rotating.
Step 2: Know the formula for angular momentum, which is L = Iω, where I is the moment of inertia and ω is the angular velocity.
Step 3: Identify the moment of inertia (I) for a disk, which is given by the formula I = (1/2)MR^2, where M is the mass and R is the radius of the disk.
Step 4: Substitute the moment of inertia into the angular momentum formula: L = (1/2)MR^2 * ω.
Step 5: Simplify the expression to find the angular momentum: L = (1/2)M R^2 ω.

Angular Momentum – Angular momentum is a measure of the rotational motion of an object, calculated as the product of its moment of inertia and angular velocity.
Moment of Inertia – The moment of inertia is a scalar value that represents how mass is distributed relative to the axis of rotation, with the formula for a solid disk being I = (1/2)MR^2.
Rotational Dynamics – Understanding the relationship between angular velocity and angular momentum is crucial in rotational dynamics.