When we think of an object moving through space, it’s easy to imagine a single mass at its center. This “single mass” is called the object’s center of gravity, and it determines how the object will move. For instance, if you hold a baseball in your hand and let go, the ball will fall straight down due to gravity acting on its center of gravity. But what if you were holding the baseball by one of its sides? It would spin as it fell. This happens because the spinning motion comes from another property known as the moment of inertia (sometimes abbreviated as “moment,” but not to be confused with torque). The more mass an object has farther away from its center axis, the greater its moment of inertia will be. So when we release that baseball held sideways, it spins because most of its weight is outside of its axisâ€”that is, farther away from our hand than where our hand touches!

## What is Moment of Inertia – Definition?

The **moment of inertia** is a physical quantity that determines how much torque is needed for a certain angular acceleration about a rotational axis, similar to how mass dictates how much force is needed for a certain acceleration.

## Moment of Inertia Formula – Triangle, Rectangle, and Other Shapes

The moment of inertia (MOI) is a measure of an object’s resistance to rotational acceleration. It determines how easy an object is to rotate. For example, if you have two objects with different shapes but the same mass, they will both have the same weight when hanging from a string. But the one with more surface area will be easier to spin because it has more resistance to turning compared to its smaller counterpart. This means that larger objects generally require more force to start or stop them spinning than smaller ones doâ€”which makes sense since you can easily spin a ping pong ball on your finger but not a bowling ball!

The formula for calculating the moment of inertia is:

I = \frac {L}{\omega}## Moment of Inertia Units

The units of the moment of inertia are kilograms meters squared or kg m^2. This means that if you have an object with a mass of 100kg and it is spinning at a rate of 20 radians per second (or about 2 rotations every second), then its moment of inertia would be 1,000kg m^2.

You should note that this calculation assumes the object is only rotating around one axis; if it was rotating in another direction then you would need to include those moments as well.

## How to use the moment of inertia calculator

With our moment of inertia calculator, all you have to do is pick the shape of the object in question, input its measurements, and the calculator will give you its moment of inertia.

## FAQ

### What is the moment of inertia?

The moment of inertia is a physical quantity that determines how much torque is needed for a certain angular acceleration about a rotational axis, similar to how mass dictates how much force is needed for a certain acceleration.

### What is the SI unit of moment of inertia?

The SI unit for the moment of inertia is kg/m^{2}.

### What is the moment of inertia equation for a rectangle?

If the axis passes through its center, the formula is I = bh^{3} / 12.