If you’re having difficulty determining the second moment of area of a hexagon, a circle or any other common shape, this moment of inertia calculator can help you out. Read on to learn how to use this calculator along with more information about the moment of inertia.
How to use the moment of inertia calculator?
Using this moment of inertia calculator is very easy. You can use it to find the inertia of a circle or for other shapes as long as you have the required values for the area moment of inertia calculator to perform the calculations. Here are the steps for you to follow:
- First, select the Shape from the drop-down menu. The choices are Triangle, Rectangle, Semi-circle, Circle, Ellipse, and Regular Hexagon.
- Then enter the value of the Base and choose the unit of measurement from the drop-down menu.
- Finally, enter the value of the Height and choose the unit of measurement from the drop-down menu.
- After entering all of the required values, the moment of inertia automatically generates for you the values of Ix and Iy.
What is moment of inertia in simple terms?
Moment of inertia is a commonly used concept in physics. This is also known as “angular mass” and it refers to a rotating body’s inertia with respect to its rotation. In simpler terms, the moment of inertia refers to the resistance of a rotating body to angular deceleration or acceleration.
This value is equal to the product of the object’s mass and the square of the object’s perpendicular distance from its rotational axis. You can find the value for the moment of inertia by hand or you can use a moment of inertia calculator.
What is moment of inertia of a body?
The moment of inertia is usually assigned the symbol “I.” As aforementioned, this refers to the rotational angle of an object’s mass. When it comes to Newtonian physics, the moment of inertia refers to the acceleration of a body which has an inverse proportion to its mass.
Also, in Newtonian rotational physics, the angular acceleration of a body has an inverse proportion to the body’s moment of inertia. Therefore, you may think of the moment of inertia of a body as the body’s ability to resist torque or force that’s twisting.
What is the moment of inertia of an object?
You can find the moment of inertia of an object using this area moment of inertia calculator. The moment of inertia of an object refers to a calculated measure for any given rigid body that’s rotating around a fixed axis. Therefore, this measures the difficulty of changing the rotational speed of the object.
It’s possible to calculate this measurement based on the distribution of mass within the given object along with the position of the object’s axis. This means that a single object may have varying values for the moment of inertia depending on the orientation of its axis and its location.
Conceptually speaking, you can think of the moment of inertia as a representation of a given object’s resistance to change in angular velocity. This works the same way as to how mass would represent an object’s resistance to a change in its velocity when it’s not rotating.
The calculation for the moment of inertia tells you how much force you need to speed up, slow down or even stop the rotation of a given object. The International System of Units or “SI unit” of the moment of inertia is 1 kilogram per meter-squared. Symbolically, this unit of measurement is kg-m2. When used in an equation, the moment of inertia is usually given the simple “I” or “IP.”
But how difficult would it be to rotate a given object or to move the object in a circular pattern relative to a given pivot point? The answer to this question would depend on the object’s shape and the concentration of the object’s mass. Let’s have an example to illustrate this point.
For instance, let’s assume that the resistance to change or the amount of inertia is quite low in a wheel with a central axis. Since all of the mass of this wheel is evenly distributed around its pivot point, you only need to apply a minimal amount of force on the wheel in the correct direction so you can change its velocity.
But if you tried to flip the wheel against its axis or you try to rotate something like a telephone pole, the task would be much harder. In such a case, you would need a greater amount of moment of inertia to change the object’s velocity.
What does higher moment of inertia mean?
A higher moment of inertia is an indication that you need to apply more force if you want to cause the object to rotate. Conversely, a lower moment of inertia means that you only need to apply a minimal amount of force to cause a rotation. Masses further away from the rotational axis have the highest moment of inertia.
The angular momentum of a given object, when it rotates about an axis, refers to the measure of how much rotation the object has when there aren’t any external torques applying pressure on it. Here, the torque refers to the moment of force. This is the measure of the amount of force the object needs for it to start rotating.
We consider angular momentum as a conserved quantity. This means that the value remains constant as long as there are no external torques which act upon it. This value is the product of angular velocity multiplied by the moment of inertia.
When a given object possesses an increased radius, the value of the angular velocity is low while the value of the moment of inertia is high. Examples of this are during the final and initial phase of a dive. But when the object is in the pike position, the radius of its body decreases as each of the segments move closer to the rotational axis.
In such a case, the angular velocity starts to increase while the moment of inertia decreases. Therefore, during a dive, the angular momentum remains constant which means that the moment of inertia has an inverse proportional relationship to the angular velocity.