A disk of radius R and mass M is rotating about its axis with an angular velocit
Practice Questions
Q1
A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is the angular momentum of the disk?
(1/2)MR^2ω
MR^2ω
(1/4)MR^2ω
(3/2)MR^2ω
Questions & Step-by-Step Solutions
A disk of radius R and mass M is rotating about its axis with an angular velocity ω. What is the angular momentum of the disk?
Correct Answer: (1/2)MR^2ω
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 the moment of inertia (I) for a disk. The formula for the moment of inertia of a disk rotating about its axis is I = (1/2)MR^2, where M is the mass and R is the radius of the disk.
Step 3: Substitute the moment of inertia (I) into the angular momentum formula. So, L = (1/2)MR^2ω.
Step 4: Recognize that this formula gives you the angular momentum of the disk when you know its mass (M), radius (R), and angular velocity (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, affecting how much torque is needed for a desired angular acceleration.
Rotational Dynamics – Rotational dynamics involves the study of the motion of rotating bodies and the forces and torques that influence that motion.
