# Moment of inertia of triangle about tip formula

• RussellJ
In summary, the moment of inertia of a triangle about its tip can be calculated using the formula I = (1/18) * m * h^2, where m is the mass and h is the height of the triangle. It differs from other shapes because it depends on the height of the triangle, and cannot be negative as it represents an object's resistance to rotation. The moment of inertia affects the rotational motion by determining the amount of torque needed for a certain rotational acceleration. It can also be calculated for three-dimensional objects but with a more complex formula that takes into account the object's mass distribution and moments of inertia about other axes of rotation.

## Homework Statement

Calculate the moment of inertia of a 4 blade propeller

## The Attempt at a Solution

I am assuming the propeller blades to be triangles and need a formula for the mass moment of inertia about the tip of each triangular blade. Google hasn't helped thus far. Integration isn't necessary.

Case closed. I sucked it up and did the integral.

The formula for the moment of inertia of a triangle about its tip is given by I = (1/36)bh^3, where b is the base of the triangle and h is the height. In this case, the base would be the length of the propeller blade and the height would be the distance from the base to the tip of the blade.

To calculate the moment of inertia of a 4 blade propeller, you would need to calculate the moment of inertia for each individual blade and then add them together.

It is important to note that this formula assumes a uniform density distribution and neglects any variations in thickness or curvature of the blades. If these factors are significant, a more complex integration-based approach may be needed to accurately calculate the moment of inertia.

## 1. What is the formula for calculating the moment of inertia of a triangle about its tip?

The formula for calculating the moment of inertia of a triangle about its tip is I = (1/18) * m * h^2, where m is the mass of the triangle and h is the height of the triangle. This formula assumes that the triangle is a thin, flat plate with a uniform mass distribution.

## 2. How is the moment of inertia of a triangle about its tip different from other shapes?

The moment of inertia of a triangle about its tip is different from other shapes because it depends on the height of the triangle, rather than just the shape and mass distribution. This is because the moment of inertia is a measure of an object's resistance to rotational motion, and the height of the triangle affects its distribution of mass and therefore its resistance to rotation.

## 3. Can the moment of inertia of a triangle about its tip be negative?

No, the moment of inertia of a triangle about its tip cannot be negative. It is always a positive value, as it represents an object's resistance to rotation. If the triangle is rotating in the opposite direction, the sign of the moment of inertia will simply change to indicate the direction of rotation.

## 4. How does the moment of inertia of a triangle about its tip affect its rotational motion?

The moment of inertia of a triangle about its tip affects its rotational motion by determining how quickly it will rotate in response to an applied torque. A larger moment of inertia means that more torque is required to achieve the same rotational acceleration, while a smaller moment of inertia means less torque is required.

## 5. Can the moment of inertia of a triangle about its tip be calculated for a three-dimensional object?

Yes, the moment of inertia of a triangle about its tip can be calculated for a three-dimensional object. However, the formula would be more complex and would depend on the shape and mass distribution of the object. It would also take into account the object's moments of inertia about its other axes of rotation.