In a system of two rotating disks, if disk A has twice the moment of inertia of
Practice Questions
Q1
In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
LA = LB
LA = 2LB
LA = 4LB
LA = 1/2 LB
Questions & Step-by-Step Solutions
In a system of two rotating disks, if disk A has twice the moment of inertia of disk B and they are both rotating with the same angular velocity, what can be said about their angular momentum?
Step 1: Understand the terms. Moment of inertia (I) is a measure of how difficult it is to change the rotation of an object. Angular velocity (ω) is how fast the object is rotating.
Step 2: Identify the moment of inertia for both disks. Disk A has twice the moment of inertia of disk B, so if IB is the moment of inertia of disk B, then IA = 2 * IB.
Step 3: Note that both disks are rotating at the same angular velocity. This means ωA = ωB.
Step 4: Use the formula for angular momentum (L). Angular momentum L is calculated as L = I * ω.
Step 5: Calculate the angular momentum for both disks. For disk A, LA = IA * ωA. For disk B, LB = IB * ωB.
Step 6: Substitute the known values into the equations. Since IA = 2 * IB and ωA = ωB, we can write LA = (2 * IB) * ωB.
Step 7: Simplify the equation for disk A's angular momentum. This gives LA = 2 * (IB * ωB) = 2 * LB.
Step 8: Conclusion: Since LA = 2 * LB, disk A has twice the angular momentum of disk B.
