Rotational Inertia Four point masses problem-diagonal

In summary, the problem involves four point masses arranged in a square on a mass-less rod with a side length of 0.50 m. The rotational inertia for rotation about an axis passing through masses A and C is calculated using the equation I=mr^2, where the radius for points B and D is found to be 0.5m multiplied by the square root of 2 divided by 2. This comes from the fact that points B and D are each 0.5sin45m away from the axis, and sin45 is equal to the square root of 2 divided by 2.
  • #1
en bloc
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0
Rotational Inertia "Four point masses problem--diagonal"

Homework Statement



Four point masses of 3.0 kg each are arranged in a square on mass-less rod. The length of a side of the square is .50 m. What is the rotational Inertia for rotation about an axis passing through masses A and C?

A B


D C




Homework Equations



I=mr^2


The Attempt at a Solution



I have the solution but just don't understand it! I can't on my own find the radius if it's in a diagonal problem like this one. For B and D, the radius is .5m * [itex]\sqrt{}2[/itex] / 2.

Where does the [itex]\sqrt{}2[/itex] / 2 come from?
 
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  • #2


Points B and D are each 0.5sin45m away from the axis.OK?
 
  • #3


and sin45 = [itex]\frac{\sqrt{2}}{2}[/itex]
 

Related to Rotational Inertia Four point masses problem-diagonal

1. What is rotational inertia and how is it related to four point masses problem-diagonal?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in its rotational motion. In the four point masses problem-diagonal, the rotational inertia is used to calculate the object's moment of inertia in a diagonal direction, taking into account the mass and distance of each point mass.

2. How do you calculate the moment of inertia for the four point masses problem-diagonal?

To calculate the moment of inertia for the four point masses problem-diagonal, you can use the formula I = m1r1^2 + m2r2^2 + m3r3^2 + m4r4^2, where m is the mass of each point mass and r is the distance of each point mass from the axis of rotation. This formula takes into account the distribution of mass in a diagonal direction.

3. What is the significance of the four point masses problem-diagonal in rotational inertia?

The four point masses problem-diagonal is significant because it represents a common scenario in which an object has four point masses located at different distances from an axis of rotation. By calculating the moment of inertia using this scenario, we can better understand how an object's rotational motion is affected by its mass distribution.

4. How does the placement of the four point masses affect the moment of inertia in the diagonal direction?

The placement of the four point masses affects the moment of inertia in the diagonal direction by changing the distribution of mass. The closer the point masses are to the axis of rotation, the smaller the moment of inertia will be. On the other hand, if the point masses are located further from the axis, the moment of inertia will be larger.

5. Can the four point masses problem-diagonal be applied to real-world scenarios?

Yes, the four point masses problem-diagonal can be applied to real-world scenarios. For example, it can be used to calculate the moment of inertia for a rotating bicycle wheel, a spinning top, or a flying frisbee. By understanding the moment of inertia in these scenarios, we can better understand and predict their rotational motion.

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