A disk rotates about its axis with an angular velocity of ω. If its radius is do
Practice Questions
Q1
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum if the mass remains the same?
2ω
4ω
ω
ω/2
Questions & Step-by-Step Solutions
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled, what will be the new angular momentum if the mass remains the same?
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 given by the formula I = (1/2) * m * r^2, where m is the mass and r is the radius.
Step 3: If the radius (r) is doubled, the new radius becomes 2r.
Step 4: Calculate the new moment of inertia with the new radius: I_new = (1/2) * m * (2r)^2 = (1/2) * m * 4r^2 = 4 * (1/2) * m * r^2 = 4I.
Step 5: Since the angular velocity (ω) remains the same, substitute the new moment of inertia into the angular momentum formula: L_new = I_new * ω = 4I * ω.
Step 6: Conclude that the new angular momentum is L_new = 4L, where L is 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 proportional to the square of its radius (r), specifically I = (1/2)mr² for a solid disk.
Effect of Radius on Moment of Inertia – Doubling the radius of a disk increases its moment of inertia by a factor of four, since I is proportional to r².
