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?
Practice Questions
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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
Angular momentum L = Iω = (1/2)MR^2ω, where I = (1/2)MR^2 for a disk.
Questions & Step-by-step Solutions
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Q
Q: 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?
Solution: Angular momentum L = Iω = (1/2)MR^2ω, where I = (1/2)MR^2 for a disk.
Steps: 4
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).
