Khan Pong-Ball- Physics Tutorial
What the Hell Is Pong-Ball Physics?
Let's get one thing straight. Pong-ball physics isn't some fancy theory cooked up in a lab. It's the study of how a ball moves, bounces, and loses energy when it hits a surface. Simple. Every time that little rubber sphere slams against the floor, a bunch of physics is happening that most people ignore.
You encounter this in video games, sports science, even robotics. Understanding why a ball bounces the way it does helps you predict motion, design better equipment, or just figure out why your ping-pong shots keep flying off the table.
This tutorial breaks down the actual mechanics. No motivational garbage. Just the science.
The Core Forces at Play
Gravity
Gravity pulls the ball downward at 9.8 m/s². That's constant on Earth. Doesn't care about the ball's color, size, or how much you paid for it. When you release a pong ball, gravity is the first thing that takes over.
The ball accelerates as it falls. Velocity increases every second until something stops it—usually the ground.
Impact and the Normal Force
When the ball hits a surface, two things happen simultaneously. The surface pushes back with equal and opposite force (Newton's third law), and the ball deforms slightly before bouncing back.
This contact force is called the normal force. It's perpendicular to the surface. The harder the surface, the less deformation. A steel ball bearing barely squishes. A rubber superball flattens like a pancake for a millisecond.
Air Resistance
Yeah, air matters. A falling ball pushes air out of the way, creating drag. For small, slow-moving pong balls, this force is small. But it's not zero. Drop a ball from 10 meters and air resistance slightly reduces the terminal velocity compared to a vacuum.
For most practical calculations, beginners can ignore drag. For precision work, include it.
The Bounce Coefficient (Coefficient of Restitution)
Here's where things get interesting. When a ball bounces, it doesn't come back to the same height it fell from. Some energy gets lost. Every single time.
The coefficient of restitution (COR) tells you how bouncy a ball is. It's a ratio:
- COR = 1.0 means a perfectly elastic collision (no energy lost)
- COR = 0.0 means the ball sticks and doesn't bounce at all
- Real pong balls fall somewhere between 0.7 and 0.95
A ping-pong ball has a COR around 0.85. Drop it from 1 meter, it bounces back to about 0.72 meters. Not 1 meter. Physics doesn't negotiate.
Calculating COR
If you know the drop height and bounce height, you can find the COR:
COR = √(bounce height / drop height)
That's it. Square root of the height ratio. Drop from 2 meters, it bounces to 1 meter. √(1/2) = 0.707 COR. Drop it again from that 1 meter, it bounces to 0.5 meters. The math checks out.
Energy Loss During Bounce
Two types of energy are at war during a bounce: kinetic energy (motion) and potential energy (height). When the ball falls, potential energy converts to kinetic. On impact, some kinetic energy converts to heat and sound.
That "thump" you hear? That's energy leaving the system. The ball also deforms, which converts energy into internal friction within the material.
After each bounce, the ball has less energy. Each subsequent bounce is lower than the last. Eventually it stops. The energy doesn't disappear—it disperses into the floor, the air, and the ball itself as heat.
Comparing Common Ball Types
| Ball Type | Typical Mass | COR | Bounce Height (1m drop) |
|---|---|---|---|
| Ping-pong | 2.7g | 0.85 | ~0.72m |
| Tennis ball | 57g | 0.75 | ~0.56m |
| Superball | 45g | 0.90 | ~0.81m |
| Golf ball | 46g | 0.78 | ~0.61m |
| Basketball | 620g | 0.76 | ~0.58m |
The superball is the king of bounces. High COR, decent mass. Ping-pong balls bounce well too, but they're so light that air resistance affects them more noticeably.
Angular Momentum and Spin
Most tutorials skip this. Don't be most tutorials.
When a ball bounces with spin, everything changes. A forward spin adds extra horizontal velocity after bounce. Backspin can make a ball shoot forward faster. Sidespin curves the trajectory.
Real pong-ball physics accounts for angular velocity. The ball's rotation interacts with the contact surface. Friction at impact point can cause the ball to bounce at unexpected angles.
That's why a topspin table tennis shot is brutal. The spin interacts with the opponent's paddle. Without understanding angular momentum, you're just guessing.
Getting Started: Calculate Your Own Bounce
Here's what you actually do:
- Measure drop height in meters from the bottom of the ball to the surface
- Release the ball with zero initial velocity (just let go, don't throw)
- Record bounce height from the surface to the bottom of the ball at peak
- Calculate COR using the formula above
Do this three times for the same ball. Average your results. Single measurements are garbage because the floor might be slightly uneven or the ball might not be perfectly spherical.
Tools you need: a measuring tape, a flat surface, and a stopwatch if you want to calculate velocity too.
Calculating Velocity
Velocity after falling for time t:
v = g × t
For a ball dropped from 1 meter, fall time is about 0.45 seconds. Velocity at impact = 9.8 × 0.45 = 4.4 m/s.
To find velocity from bounce height instead:
v = √(2 × g × height)
This gives you the velocity the ball has when it leaves the surface after bouncing.
Common Mistakes People Make
- Ignoring air resistance for small balls at low speeds is fine. For precision, it's not.
- Measuring from the top of the ball instead of the bottom. Pick one and stick with it.
- Assuming COR is constant. Balls degrade. A worn tennis ball bounces lower than a new one.
- Forgetting spin. A ball with heavy backspin bounces differently than one dropped straight.
Where This Actually Matters
Video game physics engines use these exact principles to simulate bouncing balls. Engineers designing ball bearings need to understand energy dissipation. Sports equipment companies test balls against these standards.
If you're building a robot that catches objects, you need to predict bounce trajectories. If you're designing a ball return system, energy loss calculations tell you how much initial force you need.
This isn't academic nonsense. It's practical physics that shows up in real applications.
The Bottom Line
Pong-ball physics comes down to a few key concepts: gravity accelerates the ball, impact creates a normal force, and the coefficient of restitution determines how much energy is lost. Spin complicates things but follows predictable rules.
Measure your bounce heights, calculate the COR, and you can predict exactly how any ball will behave. No guessing. No hand-waving. Just physics.