Think of your typical swivel chair. If you sit on it, you might decide to start spinning. Want to spin faster? You can tuck in your arms or legs. Want to slow down? You can stretch out your arms. Without forces like air resistance, you could theoretically spin for as long as you want. Why? Let me introduce you to the concept of angular momentum.

Angular momentum is a vector. This means it has both magnitude and direction. How do you define it? To answer this question, angular momentum is an object’s angular velocity multiplied by its moment of inertia. Angular velocity is equal to an object’s angular displacement over time. Displacement is an object’s change in position. Angular displacement is just the rotational form of this. Think of it as how much your position changes when traveling in a circular path. If you start and end at the same point in a circle, your angular displacement is zero. If you start at the top of a circular path and end at the bottom, then you would have a positive or negative angular displacement depending on how you define your axes. The moment of inertia refers to an object’s ability to resist rotational acceleration. This property depends on how close an object’s center of mass is compared to the rotation axis. The axis is an imaginary line that an object revolves around.

Like I said before, angular momentum is conserved in the absence of non conservative forces including air resistance. When angular momentum is conserved, the moment of inertia and angular velocity are inversely related. Inversely related means that as one quantity goes up, the other goes down. Let’s apply this relationship to the swivel chair example. Increasing your moment of inertia by stretching out your arms decreases your angular velocity as indicated by your spinning slower. Decreasing your moment of inertia by tucking in your arms increases your angular velocity by causing the swivel chair to spin faster.