In a system of two rotating bodies, if one body has twice the moment of inertia
Practice Questions
Q1
In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
The same
Twice as much
Half as much
Four times as much
Questions & Step-by-Step Solutions
In a system of two rotating bodies, if one body has twice the moment of inertia of the other, how does their angular momentum compare if they rotate with the same angular velocity?
Step 1: Understand what moment of inertia (I) means. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Know that angular velocity (ω) is how fast something is rotating.
Step 3: Recall the formula for angular momentum (L): L = I * ω.
Step 4: Identify the two bodies. Let's call the first body Body A and the second body Body B.
Step 5: Assume Body A has a moment of inertia I and Body B has a moment of inertia 2I (twice that of Body A).
Step 6: Both bodies are rotating at the same angular velocity (ω).
Step 7: Calculate the angular momentum for Body A: L_A = I * ω.
Step 8: Calculate the angular momentum for Body B: L_B = 2I * ω.
Step 9: Compare the angular momentum: Since L_B = 2 * L_A, Body B has twice the angular momentum of Body A.
