A disk rotates about its axis with an angular velocity of ω. If its radius is do

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Question: A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum?

Options:

Correct Answer: 4Iω

Solution:

Angular momentum L = Iω, and if the radius is doubled, the moment of inertia I becomes 4I, thus L = 4Iω.

A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum?

A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum?

Correct Answer: 4L

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: Recognize that the moment of inertia (I) for a disk is dependent on its radius (r). When the radius is doubled (r becomes 2r), the moment of inertia changes.
Step 3: Calculate the new moment of inertia when the radius is doubled. The moment of inertia for a disk is I = (1/2) * m * r^2. If r is doubled, the new moment of inertia becomes I' = (1/2) * m * (2r)^2 = (1/2) * m * 4r^2 = 4 * (1/2) * m * r^2 = 4I.
Step 4: Substitute the new moment of inertia back into the angular momentum formula. The new angular momentum L' = I'ω = 4Iω.
Step 5: Conclude that if the radius is doubled, the new angular momentum is 4 times the original angular momentum.

Angular Momentum – Angular momentum (L) is the product of the moment of inertia (I) and angular velocity (ω).
Moment of Inertia – The moment of inertia (I) of a disk is dependent on its mass and the square of its radius.
Effect of Radius on Inertia – Doubling the radius of a disk increases its moment of inertia by a factor of four.