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A disc of radius R and mass M is rotating about its axis with an angular velocit
A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)
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Practice Questions
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Q1
A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)
Iω
MωR²
0.5MR²ω
MR²ω
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The moment of inertia I of a disc about its axis is (1/2)MR². Therefore, angular momentum L = Iω = (1/2)MR²ω.
Questions & Step-by-step Solutions
1 item
Q
Q: A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)
Solution:
The moment of inertia I of a disc about its axis is (1/2)MR². Therefore, angular momentum L = Iω = (1/2)MR²ω.
Steps: 5
Show Steps
Step 1: Understand that angular momentum (L) is related to the moment of inertia (I) and angular velocity (ω). The formula is L = Iω.
Step 2: Identify the shape we are dealing with, which is a disc with radius R and mass M.
Step 3: Find the moment of inertia (I) for a disc rotating about its axis. The formula for the moment of inertia of a disc is I = (1/2)MR².
Step 4: Substitute the moment of inertia (I) into the angular momentum formula. So, L = Iω becomes L = (1/2)MR²ω.
Step 5: Conclude that the angular momentum of the disc is L = (1/2)MR²ω.
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