No. Newton’s laws are vector equations, and they work equally well in two and three dimensions. For motion in a plane, we’ll focus on how a force tangent to a particle’s trajectory changes its speed, while a force perpendicular to the trajectory changes the particle’s direction.

《 LOOKING BACK Chapter 4 Kinematics of projectile and circular motion

For linear motion, one component of the acceleration was always zero. Motion in a plane generally has acceleration along two axes. If the accelerations are independent, we can use x- and y-coordinates and we will find motions analogous to the projectile motion we studied in Chapter 4.

Circular motion must have a force component toward the center of the circle to create the centripetal acceleration. In this case the acceleration components are radial and, perhaps, tangential. We’ll use a different coordinate system, rtz coordinates, to study the dynamics of circular motion.

Yes, it does. The circular orbit of a satellite or planet is motion in which the force of gravity is creating the inward centripetal acceleration. You’ll see that an orbiting projectile is in free fall.

《 LOOKING BACK Section 6.3 Gravity and weight

How can you swing a bucket of water over your head without the water falling out? Why doesn’t a car going around a loop-the-loop fall off at the top? Circular motion is not always intuitive, but you’ll strengthen your ability to use Newtonian reasoning by thinking about some of these problems.

By starting with linear motion, we were able to develop the ideas and tools of Newtonian mechanics with minimal distractions. But planes and rockets move in a plane. Satellites and electrons orbit in a plane. The points on a rotating hard drive move in a plane. In fact, much of this chapter is a prelude to Chapter 12, where we will study rotational motion. This chapter gives you the tools you need to analyze more complex—and more realistic—forms of motion.