The moment of inertia of a system of particles is calculated by summing which of the following?
Practice Questions
1 question
Q1
The moment of inertia of a system of particles is calculated by summing which of the following?
Mass times distance from the axis
Mass times square of distance from the axis
Mass times angular velocity
Mass times linear velocity
The moment of inertia is calculated by summing the mass of each particle times the square of its distance from the axis of rotation: I = Σ(m_i * r_i²).
Questions & Step-by-step Solutions
1 item
Q
Q: The moment of inertia of a system of particles is calculated by summing which of the following?
Solution: The moment of inertia is calculated by summing the mass of each particle times the square of its distance from the axis of rotation: I = Σ(m_i * r_i²).
Steps: 6
Step 1: Understand that the moment of inertia is a measure of how difficult it is to change the rotation of an object.
Step 2: Recognize that the moment of inertia depends on the mass of each particle in the system.
Step 3: Identify that the distance of each particle from the axis of rotation is important.
Step 4: For each particle, calculate the square of its distance from the axis of rotation (r_i²).
Step 5: Multiply the mass of each particle (m_i) by the square of its distance (r_i²).
Step 6: Sum all the values from Step 5 for all particles to get the total moment of inertia (I).
