What is the angular momentum of a rolling object about its center of mass?
Practice Questions
1 question
Q1
What is the angular momentum of a rolling object about its center of mass?
mv
Iω
mv + Iω
0
The angular momentum L of a rolling object about its center of mass is given by L = mv + Iω, where I is the moment of inertia and ω is the angular velocity.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the angular momentum of a rolling object about its center of mass?
Solution: The angular momentum L of a rolling object about its center of mass is given by L = mv + Iω, where I is the moment of inertia and ω is the angular velocity.
Steps: 6
Step 1: Understand that angular momentum is a measure of how much motion an object has while rotating.
Step 2: Identify the rolling object and its center of mass, which is the point where the mass of the object is balanced.
Step 3: Recognize that the total angular momentum (L) of the rolling object can be calculated using two parts: linear momentum and rotational momentum.
Step 4: The linear momentum part is given by mv, where m is the mass of the object and v is its linear velocity.
Step 5: The rotational momentum part is given by Iω, where I is the moment of inertia (a measure of how mass is distributed in the object) and ω is the angular velocity (how fast it is rotating).
Step 6: Combine both parts to find the total angular momentum: L = mv + Iω.
