# Ferris Wheel Physics

There is no better example of physics at work than to look at amusement park rides. From the mechanical engineering feats that make a roller coaster, to the physical trickery of carnival games, a fairground is the most practical example of physics in action. Take the Ferris wheel, for instance. If you have ever been on a Ferris wheel ride, you have been the subject of centripetal acceleration at work.

**How does a Ferris wheel work?**

Before you build a Ferris wheel you must first understand Ferris wheel physics. Ferris wheels are large, non-building structures that rotate about a central axis. Seats are attached to the outer rim of the wheel and always hang downwards. This is because as the Ferris wheel spins the seats, or gondolas, can freely rotate at the support where they are connected to the wheel. The Ferris wheel spins upwards with the help of gears and motors, while gravity pulls the wheel back down again. This cycle continues for the duration of the ride.

The interesting part comes into play when you realize that you feel lighter at the top of the Ferris wheel, and heavier when you are at the bottom. But how can that be? After all your mass never changes at different points during the revolution; that is where centripetal acceleration comes into play.

**Physics 101: Terminology**

To learn how a Ferris wheel works we first need to understand some basic physic terms:

**Acceleration:** The rate of change of velocity with respect to time. If an object is speeding up, slowing down, or changing direction, it is accelerating or decelerating. Acceleration describes the rate of change of both the magnitude and the direction of velocity. Acceleration = Force divided by mass or a=F/m.

**Force:** An influence on an object which causes a change in velocity, direction, or shape. Force equals mass times acceleration or F=ma.

**Gravity:** The force that tends to draw objects towards the center of the Earth.

**Mass:** The amount of matter within an object is called **mass**. The terms mass and **weight** are often used interchangeably. However, weight=Mass x Gravity, thus mass can never be zero while weight can be zero when no gravitational forces are acting upon it, such as in outer space.

**Inertia:** The tendency to resist change in motion. Inertia is the embodiment of Newton’s first law: *an object at rest stays at rest and an object in motion stays in motion with the same speed and the in the same direction unless acted upon by an unbalanced force.*

To explain this, let’s think about an environment free of gravity (a force) like space. If you throw a ball in space, it will theoretically fly through the air forever in the exact direction and the exact same speed with which you threw in. However, if it came into contact with an unbalanced force such as a meteor, it would change its direction

**Centripetal Acceleration:** The definition for centripetal acceleration is: *the acceleration toward the center that holds a satellite elliptical in orbit. *In Laymen’s terms, it is the force that keeps a smaller object orbiting a bigger one. Think of it like the solar system. The Earth orbits the Sun thanks to centripetal acceleration. The equation for centripetal acceleration is: a = W2*R, where W presents the angular velocity of the Ferris wheel in radians and R is the radius of the Ferris wheel. Thus you can see how important it is for an observation wheel with a large radius to turn slowly because the rotation rate will have a significant impact on the centripetal acceleration.

**How does this apply to Ferris wheels?**

A typical Ferris wheel rotates at a constant speed (unless stopping to let passengers off). But velocity is speed with a direction vector attached to it, so velocity is changing every second. Your bodies’ “apparent” weight varies depending on the place you are on the ride. You can feel your “true weight” when the centripetal acceleration is pointing horizontally and has no vector component parallel with gravity. It has no contribution in the vertical direction so this is affected when you are exactly halfway between the top and bottom.

At these two positions centripetal acceleration presents a vector which is parallel with gravity, so they can be directly added together.

### Force at the Top of the Wheel

At the top of the circle centripetal acceleration is pointing directly down. F1 is the force exerted on the passengers at the top of the wheel. **F1=m(g-a)**. Standing on the Earth we are at 1g. At the top of the Ferris wheel the passengers may experience 0.5g, thus they feel lighter (but remember their mass is the same).

### Force at the Bottom of the Wheel

When you reach the bottom of the Ferris wheel, the ride becomes more exciting because of the fact that both forces, rotation and weight combine what results in greater acceleration or g force, meaning you feel heavier. At the bottom of the circle centripetal acceleration, which always points towards the center of the circle, is pointing directly up. F2=m(g+a). At the bottom of the Ferris wheel the passengers experience 1.5g and they feel heavier.

### Conclusion

Those are just a few of the forces at work on a Ferris wheel. There is much to be learned from amusement parks other than pure entertainment. Now that we understand Ferris wheel physics, we can begin to learn how to build and operate one safely. Read more about Observation Wheel Technology.