Moment of Inertia of 4 Balls on Square Side

In summary, the conversation discusses finding the moment of inertia of a system consisting of four solid balls with equal mass and radius at the corners of a square. The participant uses the parallel axis theorem to calculate the moment of inertia, but questions why the answer also includes the moment of inertia for two balls along the axis. It is clarified that the participant did not initially consider the moment of inertia for these two balls, leading to the discrepancy.
  • #1
erisedk
374
7

Homework Statement


There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius is r. Find the moment of inertia of the system about one of the sides of the square.

Homework Equations

The Attempt at a Solution


I= 2 (two balls) × [ 2/5 mr^2 (Icm) + ma^2 ] (just used parallel axis theorem)

However, in the answer,
I = 2 ( 2/5 mr^2 ) + 2×[ 2/5 mr^2 + ma^2 ]

Why have they added 2 ( 2/5 mr^2 ) ??
 
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  • #2
Using the parallel axis theorem is good. I don't see it under 2. What does it look like and for what balls do you apply it ?
 
  • #3
erisedk said:
There are four solid balls

Why have they added 2 ( 2/5 mr^2 ) ??
Consider the above two lines.
 
  • #4
Ok, right!
I got it, thanks. I didn't consider moi of the two balls along the axis.
 

1. What is moment of inertia?

Moment of inertia is a measure of an object's resistance to rotational motion. It depends on the mass and distribution of the object's mass relative to its axis of rotation.

2. How is moment of inertia calculated?

The moment of inertia for a system of objects can be calculated by summing the individual moments of inertia for each object. The formula for moment of inertia is I = Σmiri2, where mi is the mass of each object and ri is the distance from the object to the axis of rotation.

3. Why is moment of inertia important?

Moment of inertia is important because it helps determine the amount of torque needed to rotate an object. It also affects an object's angular acceleration and stability.

4. How does the arrangement of objects affect moment of inertia?

The arrangement of objects can greatly affect the moment of inertia. For example, objects placed further from the axis of rotation will have a larger moment of inertia compared to objects placed closer to the axis.

5. What is the moment of inertia of 4 balls on a square side?

The moment of inertia for this specific system of objects can be calculated using the formula for a thin rod rotating about its center of mass. This would result in a moment of inertia of I = (1/12)MR2, where M is the total mass of the 4 balls and R is the distance from the center of the square to the balls.

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