Circular motion is a little different from straight-line motion in a few different ways. Objects that move in circles are roller coasters in a loop, satellites in orbit, DVDs spinning in a player, kids on a merry go round, solar systems rotating in the galaxy, making a left turn in your car, water through a coiled hose, and so much more.

Imagine driving your car in a circle, like you would when take a clover-leaf type of freeway exit, or make a right turn on a green light. Here’s how the forces play out during the motion:

For any object that goes in a circle (or you can approximate it to a circle), you’ll want to use this approach when solving problems. You can feel the effect of circular motion if you’ve ever been in a car that suddenly turns right or left. You feel a push to the opposite side, right? If you are going fast enough and you take the turn hard enough, you can actually get slammed against the door. So my question to you is: who pushed you? Let’s find out!

An object that moves in a circle with constant speed (like driving your car in a big circle at 30 mph) is called uniform circular motion. Although the speed is constant (30 mph), the velocity, which is a vector and made up of speed and direction, is not constant. The velocity vector has the same speed (magnitude), but the direction keeps changing as your car moves around the circle. The direction is an arrow that’s tangent to the circle as long as the car is moving on a circular path. This means that the tangent arrow is constantly changing and pointing in a new direction.

Now this next experiment is a little dangerous (we’re going to be spinning flames in a circle), so I found a video by MIT that has a row of five candles sitting on a rotating platform (like a “lazy susan”) so you can see how it works.

The candles are placed inside a dome (or a glass jar) so that when we spin them, they aren’t affected by the moving air but purely by acceleration. So for this video above, a row of candles are inside a clear dome on a rotating platform. When the platform rotates, air inside the dome gets swung to the outer part of the dome, creating higher density air at the outer rim, and lower density air in the middle. The candle flames point inwards towards the middle because the hot gas in the flames always points towards lower density air. Source: http://video.mit.edu

Now you’re beginning to understand how an object moving in a circle experiences acceleration, even if the speed is constant.

So what direction is the acceleration vector?

It’s pointed straight toward the center of that circle.

Velocity is always tangent to the circle in the direction of the motion, and acceleration is always directed radially inward. Because of these two things, the acceleration that arises from traveling in a circle is called centripetal acceleration (a word created by Sir Isaac Newton). There’s no direct relationship between the acceleration and velocity vectors for a moving particle.

Click here to go to next lesson on Centripetal Force.

Do you remember when I asked you “Who pushed you?”  when you were riding in a car that took a sharp turn? Well, the answer has to do with centripetal force. Centripetal (translation = “center-seeking” ) is the force needed to keep an object following a curved path.

Remember how objects will travel in a straight line unless they bump into something or have another force acting on it like gravity, friction, or drag force? Imagine a car moving in a straight line at a constant speed. You’re inside the car, no seat belt, and the seat is slick enough for you to slide across easily. Now the car turns and drives again at constant speed but now on a circular path. When viewed from above the car, we see the car following a circle, and we see you wanting to keep moving in a straight line, but the car wall (door), moves into your path and exerts a force on you to keep you moving in a circle. The car door is pushing you into the circle.

According to Newton’s second law of motion, if you are experiencing an acceleration you must also be experiencing a net force (F=ma). The direction of the net force is in the same direction as the acceleration, so for the example with you inside the car, there’s an inward force acting on you (from the car door) keeping you moving in a circle.

If you have a bucket of water and you’re swinging it around your head, in order to  keep a bucket of water swinging in a circle, the centripetal force can be felt in the tension experienced by the handle. Swinging an object around on a string will cause the rope to undergo tension (centripetal force), and if your rope isn’t strong enough, it will snap and break, sending the mass flying off in a tangential straight line until gravity and drag force pull the object to a stop.

This force is proportional to the square of the speed, meaning that the faster you swing the object, the higher the magnitude of the force will be.

Remember Newton’s First Law? The law of inertia? It states that objects in motion tend to stay in motion with the same speed and direction unless acted upon by an unbalanced/external force. Which means that objects naturally want to continue going their straight and merry way (like you did in a straight line when you were inside the car) until an unbalanced force causes it to turn speed up or stop. Can you see how an unbalanced force is required for objects to move in a circle? There has to be a force pushing on the object, keeping in on a circular path because otherwise, it’ll go off in a straight line!

Every object moving in a circle will experience a force pushing or pulling it toward the center of the circle. Whether it’s a car making a turn and the friction force from the road are acting on the wheels of the car, or a bucket is swung around your head and the tension of the rope keeps it moving in a circle, they all have to have a force keeping them moving in that circle, and that force is called centripetal force. Without it, objects could never change their direction. Because centripetal force is tangent to the velocity vector, the force can change the direction of an object without changing the magnitude.

Let’s do a sample problem involving a car:

Now let’s do a similar problem but this time with a kid instead of a car:

I love amusement park rides, even though I know what’s going on from the science side of things! Here’s one that’s always been a favorite of mine:

Before we go any further, we need to take a look at how friction gets handled in these types of problems:

You’ve come so far with your analysis that I really want to give you the “real way” to solve these types of problems. Normally, this method isn’t introduced to you until your second year in college, and that’s only if you’re an engineer taking Statics and Dynamics classes (the next level after this course).

Here’s a step-by-step method that really puts all the pieces we’ve been working on all together into one:

Let’s do something fun now… want to know about the physics of real roller coasters?

There’s two main types of maneuvers a roller coaster can do that’s easy for us to analyze with uniform circular motion: camel-backs are the first one:

We’re going to build monster roller coasters in your house using just a couple of simple materials. You might have heard how energy cannot be created or destroyed, but it can be transferred or transformed (if you haven’t that’s okay – you’ll pick it up while doing this activity).

Roller coasters are a prime example of energy transfer: You start at the top of a big hill at low speeds (high gravitational potential energy), then race down a slope at break-neck speed (potential transforming into kinetic) until you bottom out and enter a loop (highest kinetic energy, lowest potential energy). At the top of the loop, your speed slows (increasing your potential energy), but then you speed up again and you zoom near the bottom exit of the loop (increasing your kinetic energy), and you’re off again!

Here’s what you need:

You can find circular motion everywhere, including football, car racing, ice skating, and baseball.  An ice skater spins on ice, or a competition speed skater makes a turn… they are both examples of circular motion. A turn happens when there’s a force component directed inward from the circular path. Let me show you a couple of examples:

What about your car along a circular path? Let’s take a look at two different examples. The first is an unbanked turn with friction:

The second example is a banked turn, like NASCAR racing: