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 while keeping the mass constant, what will be the new angular momentum?
2Iω
4Iω
Iω
I(2ω)
Questions & Step-by-Step Solutions
A disk rotates about its axis with an angular velocity of ω. If its radius is doubled while keeping the mass constant, what will be the new angular momentum?
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: Know that the moment of inertia (I) for a disk is proportional to the square of its radius (r). This means if the radius is doubled (2r), the new moment of inertia becomes I' = 4I (since (2r)^2 = 4r^2).
Step 3: Since the mass of the disk remains constant, we only need to consider the change in radius affecting the moment of inertia.
Step 4: Substitute the new moment of inertia into the angular momentum formula: L' = I'ω = 4Iω.
Step 5: Conclude that 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), expressed as L = Iω.
Moment of Inertia – The moment of inertia (I) of a disk is proportional to the square of its radius (r), specifically I = (1/2)mr^2 for a uniform disk.
Effect of Radius on Moment of Inertia – Doubling the radius of the disk increases the moment of inertia by a factor of four, since I is proportional to r^2.
