Center of mass of right triangle, without calculus

In summary, the formula for finding the center of mass of a right triangle without using calculus is (1/3)*(base)*(height). The center of mass is located at the intersection of the three medians, which are drawn from each vertex to the midpoint of the opposite side. It cannot be located outside of the triangle and is affected by the shape of the triangle. The center of mass can also be used to find the moment of inertia using the parallel axis theorem.
  • #1
al_9591
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Homework Statement


How can I find the center of mass of a right triangle, of height h, length a, and mass m, without using calculus?

Homework Equations


The Attempt at a Solution


I just need a hint on how to start please
 
Last edited:
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  • #2
Hint: The CM is anywhere on a line splitting the triangle into two equal masses. If you can find a second such line, the CM will be at the intersection of the two lines.
 

Related to Center of mass of right triangle, without calculus

1. What is the formula for finding the center of mass of a right triangle without using calculus?

The formula for finding the center of mass of a right triangle without using calculus is (1/3)*(base)*(height), where the base is the length of the bottom side of the triangle and the height is the length of the side perpendicular to the base.

2. How does the center of mass of a right triangle relate to its vertices?

The center of mass of a right triangle is located at the intersection of the three medians, which are line segments drawn from each vertex to the midpoint of the opposite side.

3. Can the center of mass of a right triangle be located outside of the triangle?

No, the center of mass of a right triangle will always be located within the triangle, specifically at the intersection of the three medians.

4. Does the shape of a right triangle affect the location of its center of mass?

Yes, the location of the center of mass of a right triangle is dependent on its shape, specifically the length of the base and height. A longer base or height will result in a center of mass that is closer to that side.

5. Can the center of mass of a right triangle be used to find its moment of inertia?

Yes, the center of mass of a right triangle can be used to find its moment of inertia by using the parallel axis theorem, which states that the moment of inertia of a shape can be calculated by adding the moment of inertia about its center of mass and the product of its mass and the square of the distance between its center of mass and the axis of rotation.

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