Rolling Ball Physics

Find out what rolling ball physics are at play when your RBS is in motion.

A rolling ball sculpture works by repeatedly controlling the energy, speed and direction of a moving ball. Gravity provides most of the motion, but getting a sculpture to run reliably requires much more than simply pointing a track downhill.

When I build a rolling ball sculpture, I am constantly working with gravity, momentum, friction, potential and kinetic energy, centripetal force, track geometry and the mass of the ball. A small change in track height, slope or radius can completely change what happens farther down the sculpture.

The ball lift gives the ball gravitational potential energy by carrying it to the top of the sculpture. Once released, gravity takes over. As the ball descends, that stored energy becomes motion. Tracks, curves, loops, drops, switches and other mechanisms control where that energy takes the ball.

After building rolling ball sculptures since 2003, much of this becomes intuitive. I can often look at a section of track and anticipate how the ball will behave, but every new sculpture still involves building, testing and adjusting until the movement works the way I want it to.

These are the main physical principles at work in a rolling ball sculpture:

Gravity: Gravity is what powers most of the movement in a rolling ball sculpture. The ball lift raises the ball and gives it gravitational potential energy. Once the ball is released onto the track, gravity accelerates it downhill. Track slope is critical: too little and the ball may stop; too much and it can gain more speed than the next element can handle.

Friction and Rolling Resistance: As a ball rolls along the track, some of its energy is lost through friction, rolling resistance, vibration and sound. These losses may seem small, but over a long section of track they matter. When I build a sculpture, I have to provide enough slope to keep the ball moving reliably without allowing it to become excessively fast.

Kinetic energy: A moving ball has kinetic energy in both its forward motion and its rotation. As the ball descends, gravitational potential energy is converted into kinetic energy and the ball generally speeds up. That energy can then carry the ball through curves, loops, jumps and other elements or be transferred into a mechanical device.

Potential energy: The higher a ball is in the sculpture, the more gravitational potential energy it has. The ball lift restores this energy by carrying the ball from the bottom of the sculpture back to the top. From there, the sculpture gradually spends that stored energy as the ball works its way downward through the track.

Momentum: Momentum depends on both the mass and velocity of the ball. I use momentum when a ball needs to operate a switch, tipping arm, strike an object or pass through an element without stopping. Too little momentum and the mechanism may not operate; too much and the ball can bounce, leave the track or hit the next section too hard.

Curves, Loops and Centripetal Force: Whenever a ball follows a curved path, it must continuously change direction. That requires an inward, or centripetal, force. The required force increases with the ball's mass and with the square of its speed and decreases as the curve becomes larger. This is especially important when I build tight turns, loops and spirals. A ball entering a curve too quickly may leave the track, while one entering a loop too slowly may not complete it.

Energy transfer: Rolling ball sculptures constantly transfer energy from one form to another. A descending ball converts gravitational potential energy into translational and rotational kinetic energy. It can then transfer some of that energy to switches, tipping arms, bells or other moving elements. Eventually the ball reaches the bottom, where the lift adds energy to the system and raises it again so the cycle can repeat.

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Rolling Ball Sculptures: A Study in the Science of Motion.

“One of the fascinating things about Matthew's sculptures is that the physics isn't hidden. You can actually watch gravity, momentum and energy transfer happening in front of you. A ball accelerates down a track, changes direction through a curve, transfers energy into a mechanism, and then continues on its way.

That makes the sculptures interesting from both an artistic and scientific perspective. You don't need to know the equations to understand what is happening — you can see cause and effect every time a ball moves through the sculpture.”

— Dr. Curry, physician and longtime observer of Matthew's work See how these principles become part of a custom rolling ball sculpture, designed and built for a specific space.