33 Centripetal Forces
So far, we have only addressed motion subject to constant forces. We now turn to what happens when the forces being applied are not constant. A non-constant force can vary with time either in magnitude, or in direction. We start by looking at what happens when a force is constant in magnitude while allowing its direction to vary.
Exercise 33.1: Turn! Turn! Turn!
Now consider this scenario: the car starts out moving in the 
direction. You push it up along the 
direction, so the car “turns left” a bit. You keep this up, constantly pushing the car to the left. The car ends up “constantly turning left”, meaning: the car drives around in a circle.
At this point, we have figured out that an object moving in circular motion must be experiencing a force that points radially inwards. As it turns out, if the object is moving at constant speed, it follows that this radial force must be constant in magnitude. Can you see why?
Hint: You don’t need algebra to solve this bit. Rather, rely on the symmetry of the problem: if someone came in and sneakily rotated the whole thing with you knowing, you shouldn’t be able to tell.
Bottom line: An object moving in a circle at constant speed is subject to a force that:
- is constant in magnitude;
- always points towards the center of the circle.
When an object moves around in a circle at constant speed we refer to that motion as uniform circular motion. The center-pointing force that produces this motion is referred to as a centripetal force, and the corresponding acceleration is called the centripetal acceleration.
WARNING: “Centripetal force” is not a force in the sense that friction or tension are forces. Rather, “centripetal” is more like a title that describes the force’s job.
Think of it like this: there is no one person who is “the President.” “President” is a title bestowed on a person based on that person’s job. Same thing with centripetal forces. There are a variety of forces like tension, or gravity, or friction; any of them can be a “centripetal force” if their job is to keep an object moving in a circle.
Let’s illustrate this last point with a couple of different examples.
Exercise 33.2: Identify the centripetal force
The point here is this:
There is no such thing as a centripetal force.
Rather, “centripetal” is a title that we can confer on the physical forces we know and love.
Key Takeaways