Moment of inertia of 3-mass system

In summary, the problem involves a 3-mass system with an axis of rotation perpendicular to the system. The masses are separated by rods of length 3 m and the entire length is 6 m. The second part asks for the moment of inertia of the system about a new axis passing through a point at a distance of 2.3 m from the leftmost mass. The equation used to solve this is I= \summiri2, and the final answer is 98.99 kg · m2.
  • #1
DrMcDreamy
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Homework Statement


This is a two part problem, I answered the first but was wondering if I did the second part right.

a) Consider a rigid 3-mass system (with origin at the leftmost mass 3 kg) which can rotate about an axis perpendicular to the system. The masses are separated by rods of length 3 m, so that the entire length is 6 m. 3.8

b) Now consider a rotation axis perpendicular to the system and passing through the point x0 at a distance 2.3 m from the leftmost mass 3 kg.
Find the moment of inertia of the 3-mass system about the new axis. Answer in units of kg · m2.

Homework Equations



I= [tex]\sum[/tex]miri2

The Attempt at a Solution



I= (3 kg)(2.3)2 + (2 kg)(.7)2 + (6 kg)(3.7)2 = 98.99

Is this correct?
 
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  • #2
Forget it, I realized my work is right :smile:
 

1. What is moment of inertia?

Moment of inertia is a physical property of a system that describes how resistant it is to changes in its rotational motion. It is a measure of the distribution of mass around an axis of rotation.

2. How is moment of inertia calculated?

The moment of inertia of a 3-mass system can be calculated by summing the products of each mass's mass and the square of its distance from the axis of rotation. The equation is I = m1r1^2 + m2r2^2 + m3r3^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.

3. What is the significance of moment of inertia in rotational motion?

Moment of inertia plays a crucial role in rotational motion as it determines how much torque is needed to produce a certain amount of angular acceleration. It also affects the stability and ease of rotation of an object.

4. How does the distribution of mass affect the moment of inertia?

The moment of inertia is directly proportional to the mass and the square of the distance from the axis of rotation. This means that the more mass an object has and the further away it is from the axis, the higher the moment of inertia will be.

5. Can the moment of inertia of a 3-mass system change?

Yes, the moment of inertia can change if there is a change in the distribution of mass in the system or if the axis of rotation is changed. The moment of inertia is a dynamic property that can vary depending on the conditions of the system.

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