- #1
In summary, the speaker is seeking help in finding the moment of inertia of an equilateral triangle about its center and its tip. They mention their current approach of splitting the triangle into two right triangles and integrating from 0 to root 3 over 2A, but believe there is an easier method. The suggested solution is to calculate the moment of inertia about the center of mass and add the product of the triangle's mass and 2/3 the length of the median from the vertex to the base. The speaker expresses uncertainty about their calculation of 7/12 MA^2 and seeks confirmation.
- #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!
Hi joserse46! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help!
Hi joserse46! Welcome to PF!
Show us what you've tried, and where you're stuck, and then we'll know how to help!
- #3
joserse46
- 4
- 0
Well what I am doing now is splitting the triangle up into two right triangles and finding the RI of on about it's tip (the tip that makes the right anlge), from there I could use the rod about the tip the intergrate from 0 to root 3 over 2A (the length og the triangle) But I sure there is an easier way to do this>
- #4
Bob S
- 4,662
- 7
First, calculate the moment of inertia about its center of mass, which is at the intersection of the three medians (drawn from each vertex to the center of the opposite side). Now add to this moment of inertia the product of the triangle's mass times 2/3 the length of the median from the vertex to the base. This latter term is called the Principal Axis Theorem.
- #5
joserse46
- 4
- 0
well i came to 7/12 MA^2 but that doesn't seem right since I know for a fact that it's 5/12MA^2 about it's tip and 1/12MA^2 about it's center. so shouldn't it be between that or I'm assuming too much
Hope someone can confirm this
Hope someone can confirm this
1. What is rotational inertia of a triangle?
Rotational inertia of a triangle is a measure of an object's resistance to changes in its rotational motion. It is also known as moment of inertia and is influenced by the shape, size, and mass distribution of the triangle.
2. How is rotational inertia of a triangle calculated?
The formula for calculating rotational inertia of a triangle is I = (1/12) * m * h^2, where I is the rotational inertia, m is the mass of the triangle, and h is the height of the triangle. This formula assumes that the triangle is rotating around its center of mass.
3. What factors affect the rotational inertia of a triangle?
The rotational inertia of a triangle is affected by its mass, size, and shape. Objects with larger mass, greater size, and more spread-out mass distribution have a higher rotational inertia. The distance of the object's mass from the axis of rotation also affects its rotational inertia.
4. How does rotational inertia of a triangle relate to its rotational motion?
The higher the rotational inertia of a triangle, the more force is required to change its rotational motion. This means that an object with a higher rotational inertia will take more effort to start, stop, or change its rotational speed compared to an object with a lower rotational inertia.
5. What are some real-life examples of rotational inertia of a triangle?
Some examples of rotational inertia of a triangle in real life include a spinning top, a bicycle wheel, and a figure skater spinning on the ice. These objects have a certain shape and mass distribution that affects their rotational inertia and how they behave in motion.
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