Angular Momentum Explained in Simple Words

Angular momentum is a property of the rotational motion of an object. It quantifies the tendency of an object to keep rotating around a particular point or axis. Let's try to better understand angular momentum with an example. Imagine you are on a merry-go-round on a playground. As the ride picks up speed, you feel your grip tightening on the handle because you feel like you are being pushed outwards. Now, what causes that feeling? Here's another example. You may have seen ice skaters perform various stunts and tricks on television. In one of their moves, wherein they spin very fast, you may have noticed that they start with their arms outstretched, but then pull their arms close to their body before beginning to spin so fast that it makes your head, well, spin. Both of these examples are related to how angular momentum works. Simply put, angular momentum is a measure of the rotational motion contained in an object that is revolving or rotating around a point or an axis. It is calculated as the product of the moment of inertia and the angular velocity of the object. Similar to linear momentum, which applies to objects in linear motion or moving in a straight line, angular momentum applies to objects that are rotating or revolving. The mathematical formula for angular momentum is similar to that of linear momentum. While linear momentum is the product of an object's mass and velocity, angular momentum is the product of the moment of inertia and the angular velocity of the object. The moment of inertia can be considered as rotational mass, telling us how the mass is distributed relative to the axis of rotation. It's important to note that angular momentum is a vector quantity, which means that it has both magnitude and direction. The direction of the angular momentum vector is determined by the right-hand rule. This means that if you point your fingers in the direction of the rotational motion of the object, your thumb will provide the direction of the angular momentum vector in a three-dimensional space. Here's another important insight about angular momentum. The total angular momentum of a closed system remains constant if no external torque is applied. Let's break this down a bit further. We call a system closed when no external forces influence it in any way. In a closed system consisting of one or multiple objects, the total angular momentum is equal to the sum of the angular momenta of all individual objects within that system. If nothing from outside influences this system, or in other words, no external forces act on it, then the total angular momentum doesn't change. It retains its value unless something external affects it. This is known as the law of conservation of angular momentum. The law of conservation of angular momentum has numerous practical applications in our daily lives. Let's consider the ice skater, the example we discussed at the start of this video. When the ice skater pulls their arms in, their moment of inertia decreases. Since no other major forces are acting on them, their angular momentum remains conserved, causing their rotational velocity to increase. Therefore, the skater is able to increase their rotational speed by temporarily redistributing their mass around the axis of rotation. Consider a diver jumping off a springboard. Just after they jump, they may start to rotate or perform a somersault. This makes their body more compact, resulting in a decrease in their moment of inertia. As a result, their rotational velocity increases, causing them to spin faster temporarily. However, right before they touch the water's surface, they extend their arms and legs, thereby increasing their moment of inertia. This reduces their rotational velocity, but the total angular momentum remains conserved, so they impact the water's surface relatively slowly compared to when they were somersaulting through the air. This law also applies to massive celestial bodies in our universe. For example, the planets in our solar system revolve around the sun in elliptical paths. When they reach the point in the orbit where they are relatively closer to the sun, they speed up. This is because the planet's moment of inertia is lower when it's closer to the sun, and the speed increases to keep the angular momentum constant. The next time you find yourself spinning on a merry-go-round, tossing a frisbee, or admiring a figure skater's smooth spins, remember that you're observing angular momentum at work, the fundamental principle of physics that elegantly connects motion, force, and rotation throughout the universe.