Calculating Moment of Inertia for Square Particle System

In summary, the moment of inertia of the system through a perpendicular axis at the center of the square, with four masses of 30gr at the vertices and a square side length of 90cm, can be calculated using the formula I = mr^{2}. The distance from the axis of rotation will be the hypotenuse of a right triangle with sides of 45cm, and the result should be multiplied by 4. This is a correct solution.
  • #1
duplaimp
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Homework Statement


There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm.
What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?

The Attempt at a Solution


My idea is to use the moment of inertia [itex]I = mr^{2}[/itex] (Point mass m at a distance r from the axis of rotation.)
Then the distance will be the hypotenuse of a right triangle that has each side with 45cm and putting that into the moment of inertia and multiply by 4

Is this correct?
 
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  • #2
Yes, that is correct.
 
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  • #3
Thank you
 

Related to Calculating Moment of Inertia for Square Particle System

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is similar to mass in linear motion.

2. How is moment of inertia calculated for a square?

For a square, the moment of inertia is equal to (1/12) * m * a^2, where m is the mass of the square and a is the length of one side.

3. Why is moment of inertia important?

Moment of inertia is important because it helps us understand how objects will rotate when subjected to external forces. It is also used in engineering and physics to design structures and machines.

4. How does the moment of inertia change with different shapes?

The moment of inertia varies depending on the shape of an object. Objects with a larger mass and/or a larger distance from the axis of rotation will have a larger moment of inertia. In general, objects with a wider distribution of mass will have a larger moment of inertia.

5. How does the moment of inertia affect an object's rotational motion?

The moment of inertia determines how much torque is required to change an object's rotational motion. Objects with a larger moment of inertia will require more torque to achieve the same angular acceleration as objects with a smaller moment of inertia.

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