In a way, a game like basketball is a physics geek's delight. It's a playground where you can apply physics principles to try and get some added insight to the game. You've got the interplay of projectile motion and collisions, energy and momentum, and so on. To get you started, here's a list of five neat pieces of physics that you may not typically think about when watching a game.

1. Whenever you jump, you spend 71 percent of your time in the top half of the jump. This helps create the floating illusion of hangtime.

You might expect that when you jump, you spend equal amounts of time in the top and the bottom half of your jump.

But if you think about it, you're moving fastest the moment you leave the ground. Every instant after liftoff, you slow down, until you reach zero vertical speed for a brief instant at the peak of your jump. After that, your speed increases again in the downwards direction, as you fall back down. This means that the top half of your jump (in terms of height) is also the slower half, and so it takes more time to cover that half.

How much more time? To work this out, we need to know that when you drop an object from rest, the time it takes to fall depends on the square root of the distance. The time it takes to fall half the distance is therefore just sqrt(1/2), or 71 percent the time it takes to fall the whole distance.

Basketball players appear to float because they spend 71 percent of their 'hang time' in the top half of their jump. If they're moving towards the hoop as well, then 71 percent of that horizontal distance is covered while they're in the top half of their jump, adding to the illusion of floating.

__2. To make a layup (or a moving shot), players have to account for how their speed is added to the ball's speed. __

Picture someone riding a bike in a straight line at a constant speed. They throw a ball vertically up into the air. After the ball leaves their hand, they keep cycling at the same steady pace.

From the perspective of the cyclist, does the ball land..

In front of the cyclist?

With the cyclist?

Behind the cyclist?

Pause here for a moment to make your prediction.

Decided?

Once you've made your prediction, watch the video below. The spring loaded cart represents the cyclist, and the tennis ball is launched perfectly vertically.

Were you surprised by what you saw, or did it agree with what you expected?

To see why the ball must fall back to the cyclist, let's think of an experiment conducted by Galileo in the 1600s. Picture a ship moving along, at a constant speed, just like the cyclist. Galileo dropped a rock from the mast of a moving ship, and found that it fell at the base of the mast, not behind the mast. (Other scientists believed the rock would fall behind the mast, and even claimed they'd seen that happen, but Galileo actually did the experiment to see for himself.)

But now imagine that someone was watching this experiment from the shore. From this bystander's perspective, Galileo's ship is moving sideways, and so for the rock to land at the base of the mast, the rock must move sideways as it falls. Galileo understood what others before him had not - when he lets go of the rock, in addition to its downwards motion, it continues to move sideways with the same speed as the ship.

The same physics is at play with the cyclist and the ball. The cyclist throws the ball vertically up, but the ball also travels sideways with the cyclist's speed. So when it falls, it catches up with the cyclist.

What does this have to do with basketball?

When a basketball player makes a shot while running, they're in the same situation as the cyclist. Novice players often miss their layups because they tend to push the ball forwards towards the hoop, instead of throwing it straight up. But a trained player knows to throw the ball up instead. Just like the cyclist, the player's forward speed is added to the ball's speed, and if they don't account for this, they'll miss the shot. Similarly, if a player moves from left to right while shooting, and aims for the center of the rim, the ball will miss and land to the right of the rim. To make any moving shot, players needs to correctly account for how their speed is added to the ball's speed.

In the days before Galileo, Aristotle believed that the natural state for things was to be at rest, and that objects could only move if something keeps pushing them. Based on this idea, I'd imagine that Aristotle was more of a slam dunker than a long-range shooter, and his layups were probably pretty weak.

But Galileo had the right idea. He introduced us to the concept of inertia - the idea that objects, in the absence of any force, will keep their original speed and direction. The natural state for an object isn't rest, it's to keep moving at a constant velocity. Galileo understood that when you let go of a ball during a layup, it continues to move with your forward speed, just like the rock that he dropped from the mast of the ship. And that's why, in my mind, Galileo would have schooled Aristotle on the court any day.

3. A ball shot with backspin loses more energy on its bounce, which makes it more likely to bounce into the basket.

Basketball players are trained to shoot from their fingertips, not from their palms. This makes the ball easier to grip, but more importantly, a shot from the fingertips is automatically launched with backspin. And according to Arnold "Red" Auerbach, who's considered one of the greatest coaches in NBA's history, backspin is critical to making a shot. He says,

"The fingertips [..] help to impart backspin, which makes the shot softer and helps the shot to be "lucky" [..] A ball the strikes the rim and then stops has good backspin. Some say this is luck. But why is it that the great shooters always seem to make more of these so-called lucky shots?"

Red Auerbach was on to something here. A law of physics known as the conservation of angular momentum ensures that the ball will keep spinning at the same rate once it leaves the player's hands. But why is backspin helpful for a shooter?

To see why, first imagine a basketball that isn't spinning. When it hits the rim, the ball experiences some friction with the rim. This collision robs the ball of some of its energy, which slows it down some.

Now imagine a ball with backspin. The motion of the ball is now the sum of two different motions - the speed with which the center of the ball is flying through the air, and the spinning motion around this center. Adding those together, we find that the bottom of the ball is now moving faster than before.

This time, when the bottom of the ball strikes the rim, the collision occurs with greater speed than before. The ball experiences more friction, resulting in a greater loss of energy, and slowing the ball down more than before. From the player's perspective, a slower ball near the hoop is a good thing, because it's more likely to bounce into the hoop.

So you can see that it isn't luck, but physics, that makes shots with backspin likelier to land in the hoop.

4. Eureka! A basketball feels about 1.5 percent lighter than its true weight, because the air around it helps to lift it up.

A basketball is surrounded by air, and air pressure increases with depth. This means that the air below the ball pushes up harder than the air above it pushes down. This pressure difference creates an upwards buoyant force on the basketball. Archimedes taught us that the magnitude of this buoyant force equals the weight of the fluid (in our case, air) displaced by the object.

Plugging in numbers, we find that a basketball experiences an upwards force equal to 1.5 percent of its weight. In other words, a basketball feels lighter than its true weight, because the air around it helps to lift it up.

5. A spinning basketball deflects in its path due to uneven friction with the air.

There are four forces on a basketball as it flies through the air. You've got gravity, pulling the ball down to the Earth, the buoyant force, that's pushing the ball up, the drag force due to the air that the ball smashes into, opposing the ball's motion and slowing down. And finally, there's a fourth more subtle force, known as the Magnus force, which comes into play whenever the ball is spinning.

In 1852, Magnus wondered why cannonballs would often deflect in their path when shot out of a cannon. He realized that as the cannonball spins while flying through the air, it experiences uneven friction (or drag) with the air. This creates an unbalanced force on the cannonball, causing it to deflect sideways. (Newton, being Newton, had already worked this out about 180 years earlier, after watching Cambridge tennis players curve their shots.) Here's a nice video explainer on the Magnus effect, by Derek Muller of Veritasium.

The Magnus effect results in a small, but noticeable, curve in the motion of a spinning basketball. It's also what causes the curve of a baseball curveball.

As you can see, there's a lot that physics can teach us about science of basketball. Now, if only I could use this knowledge to improve my game.

References ———-

In writing this post, everything I learned about basketball physics comes from the following two sources:

Brancazio, Peter J. "Physics of basketball." American Journal of Physics 49.4 (1981): 356-365.

An excellent physics paper on the physics of backspin, layups, and other fun stuff.

Fontanella, John J. "The Physics Of Basketball" The Johns Hopkins University Press (2006)

This book is the authoritative reference on the physics of basketball - it's a clearly explained and delightfully empirically zealous take on the subject. If you're read this far, you'll probably enjoy this book.

Illustrations: Aatish Bhatia

Homepage image: j9sk9s via photopin cc