relates to, well, swinging a bucket over your head.
However, as you’re probably aware, the two topics have plenty to do with each other. Planetary
orbits, for instance, can be described only if you understand both gravitation and circular motion. And,
sure enough, the AP exam frequently features questions about orbits.
So let’s look at these two important topics, starting with circular motion.
Velocity and Acceleration in Circular Motion
Remember how we defined acceleration as an object’s change in velocity in a given time? Well, velocity
is a vector, and that means that an object’s velocity can change either in magnitude or in direction (or
both). In the past, we have talked about the magnitude of an object’s velocity changing. Now, we discuss
what happens when the direction of an object’s velocity changes.
When an object maintains the same speed but turns in a circle, the magnitude of its acceleration is
constant and directed toward the center of the circle. This means that the acceleration vector is
perpendicular to the velocity vector at any given moment, as shown in Figure 15.1 .
Figure 15.1 Velocity and acceleration of an object traveling in uniform circular motion.The velocity vector is always directed tangent to the circle, and the acceleration vector is always
directed toward the center of the circle. There’s a way to prove that statement mathematically, but it’s
complicated, so you’ll just have to trust us. (You can refer to your textbook for the complete derivation.)
Centripetal Acceleration
On to a few definitions.
Centripetal acceleration: The acceleration keeping an object in uniform circular motion, abbreviateda (^) c
We know that the net force acting on an object is related to the object’s acceleration by F (^) net = ma . And