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

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Question: A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)

Options:

Correct Answer: Iω

Exam Year: 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.

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)

A disc of radius R and mass M is rotating about its axis with an angular velocity ω. What is its angular momentum? (2020)

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.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation, calculated for a disc as (1/2)MR².
Angular Momentum – Angular momentum is the product of the moment of inertia and angular velocity, represented as L = Iω.