Centrifugal force: Useful for animation, but not really a physics thing

If you say the words “centrifugal force” to a physicist, you’re likely to get an earful about how this force doesn’t exist. But in animation, it can be helpful to use the concept of centrifugal force to plan characters’ and objects’ reactions when they’re attached to rotating or turning objects.

When you spin a ball on the end of a string, you have to continually pull the string toward the center of the circle. This force toward the center is called centripetal force. This is a real force in physics.

The boy pulls toward him with centripetal force to make the ball go in a circle.

When you take a sharp turn with your car, your body feels as though it’s being thrown in the direction opposite the turn. This happens not because of a mysterious force, but because your body expects to keep going straight and is prevented from doing so by the door of the turning car.

So what’s the force that keeps you in the car? When your body hits the car door, the door exerts a simple, straight-line action-reaction force to keep you inside. The feeling of this force is so common that even though the force itself is nothing special, it has its own name: centrifugal force.

Anything sitting on, or riding on, or only partially attached to a turning object will fall off if it doesn’t hang on, due to the same tendency to keep going in a straight line. If you’ve ever played on a roundabout on a playground, you know this feeling. Once it gets going, if you don’t hang on tight you’ll fall off. Here, where you exert force through your hands toward the center, you actually become part of the mass the centripetal force is acting on.

Feeling the centrifugal force on the playground

Centripetal vs. centrifugal: what’s the difference?

In general, the object doing the turning gets the centripetal force, while anything that’s just along for the ride feels a (fake) centrifugal force.

If you swing a bucket full of water overhead fast enough, no water drops out. This is another example of the apparent centrifugal force, which seems to be pushing the water into the bucket as it moves around the circle.

The water stays in the bucket!

Actually, at each moment the water is trying to move in a straight line perpendicular to the center of the circle, but is prevented from doing so by the bucket. If the swing is fast enough, the water’s tendency to try and follow the straight line is greater than the effects of gravity.

The concept of centrifugal force can be used to simulate gravity in a rotating space station with a large radius. With the right rotation, a person standing on the outer rim with his/her head pointing toward the center would feel as if they were walking in Earth gravity.

Early space station design. Image courtesy of NASA

Even though centrifugal force isn’t really a thing, you can use the concept in animation to determine how your characters and props will react to centripetal forces. The reaction can be quite wild, and can add a fun or silly quality to the action in your work, especially for secondary motion.

animated children on roundabout at playground

Post Author: Michele Bousquet

Michele Bousquet is the author of Physics for Animators. A longtime animator, teacher, and writer, Michele has written more than 20 books on computer graphics. She holds a Bachelor's Degree in Mathematics and Computer Science from McGill University.