- #1
rakshit gupta
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I am unable to find it.
What is [s]motion[/s] moment of inertia of an equilateral triangle?
- Thread starter rakshit gupta
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In summary, you are unable to find the definition of moment of inertia and are advised to create your own drawing and work out the integral. The conversation also mentions the use of the parallel axis theorem to determine the moment of inertia about the center of the triangle for a thin lamina in the shape of an equilateral triangle.
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BvU
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Hello Rakshit, welcome to PF 
!
Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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!Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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- #3
Meir Achuz
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It is easier to do the integrals if you place the x-axis along the base of the pyramid, and the y-axis going vertically through the top apex.
Then you can use the parallel axis theorem to get the moment of inertia about the center of the pyramid.
Then you can use the parallel axis theorem to get the moment of inertia about the center of the pyramid.
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SteamKing
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I'm not surprised. What does "motion of inertia" even mean?rakshit gupta said:
You can determine the second moment of area for a region which is an equilateral triangle, or the mass moment of inertia for a plate or thin lamina which has the shape of an equilateral triangle.
So which are you interested in finding?
- #5
rakshit gupta
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BvU said:Hello Rakshit, welcome to PF
Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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For a thin laminaSteamKing said:
What is the moment of inertia of an equilateral triangle?
The moment of inertia of a 2D shape is a measure of its resistance to rotational motion. It is a property that depends on the shape and mass distribution of the object. In the case of an equilateral triangle, the moment of inertia is determined by the length of its sides and its mass distribution.
How is the moment of inertia of an equilateral triangle calculated?
The moment of inertia of an equilateral triangle can be calculated using the formula I = (mL^2)/6, where m is the mass of the triangle and L is the length of its sides. This formula assumes that the triangle is a thin, flat object with all of its mass concentrated at the center.
What are the units of moment of inertia?
The units of moment of inertia depend on the units used for mass and length. In the SI system, the units for moment of inertia are kg*m^2, while in the imperial system, they are slugs*ft^2.
How does the moment of inertia of an equilateral triangle compare to other shapes?
The moment of inertia of an equilateral triangle is smaller than that of a circle with the same mass and diameter. It is also smaller than that of a square with the same mass and side length. This is because the triangle has less mass concentrated at its center compared to these other shapes.
Why is the moment of inertia important in physics?
The moment of inertia is important in physics because it is a key factor in determining how an object will respond to rotational motion. It is used in calculations involving rotational energy, angular momentum, and torque. Understanding moment of inertia is essential in fields such as mechanics, engineering, and astronomy.
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