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# What is Moment of Inertia?

A moment of inertia refers to the force needed to cause a rotating object to change speeds. All rotating objects have an axis, or a point that they rotate around. Some objects require more force to change the speed of this rotation than others. Those that will change their rotational speed easily have a low moment of inertia, while those that are difficult to change have a high one.

This concept was first introduced by Swiss mathematician and physicist Leonhard Euler in 1730. He published his theory in the book titled, *Theoria Motus Corporum Solidorum Seu Rigidorum* or *Theory of the Motion of Solid or Rigid Bodies*. The formula used to calculate it is *I = k m r2*, in which *I* equals the moment of inertia, *k* equals the inertial constant that depends on the shape of the object, *m* equals mass, and *r* equals the distance between the axis and rotational mass. For bodies with an awkward shape and no apparent constant, a series of experiments can help to determine the rate.

A common example is to think of an ice skater who is spinning. As the skater begins a spin, she stretches her arms and back out and away from her body to create a slow spin. As she reaches the end of the spin, she tucks her arms in and tightens her frame, causing her to spin much more rapidly. She has consolidated her mass closer to the axis, reduced her moment of inertia, and reduced the effort needed to spin quickly. With no change in force, she is able to accelerate her rotational speed.

There are many practical applications for this measurement. Car manufacturers study it carefully to determine how quickly a car will spin out of control. The goal is to create a high moment so that the car is less likely to lose control in a spin.

Many sports also use the concept, with golf, baseball, and diving topping the list. Divers are concerned with which angles they can use to create the lowest moment and the fastest spin in order to complete the move and seamlessly enter the water. Baseball players and golfers both work to create a smooth, effective swing, to hit the ball with the correct angles and the force required to make it fly far without excessive muscle use.

## Discussion Comments

Do bicycles and gears use a moment of inertia too? I think a one-speed bike going up a hill has a high moment of inertia. It sounds like a lot more fun experimenting with spinning cars - sounds like a MythBuster episode!

It's fascinating that our minds and bodies can intuitively use something that sounds so mathematically to explain, I doubt many of the athletes mentioned pulled out their calculators before they made their moves!

Isn't it more correct to describe the increase of rotation of a skater as they bring there arms in as conservation of angular momentum rather then inertia?

Even in space, where there is no effort, or resistance to rotation, if you pulled in mass that is rotating to a closer rotation, it would also speed up.

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