# 4: Describing Motion in Multiple Dimensions

- Page ID
- 19379

Learning Objectives

- Describe motion in a 2D plane.
- Describe motion in 3D space.
- Describe motion along the circumference of a circle.

In this chapter, we will learn how to extend our description of an object’s motion to two and three dimensions by using vectors. We will also consider the specific case of an object moving along the circumference of a circle.

prelude

Jake and Madi are riding a carousel that spins at a constant rate. Madi is closer to the center of the carousel than Jake is. What can you say about their accelerations?

- Both of their accelerations are zero.
- Madi’s acceleration is greater than Jake’s.
- Jake’s acceleration is greater than Madi’s.
- Madi and Jake have the same non-zero acceleration.

- 4.2: Motion in three dimensions
- The big challenge was to expand our description of motion from one dimension to two. Adding a third dimension ends up being trivial now that we know how to use vectors. In three dimensions, we describe the position of a point using three coordinates, so all of the vectors simply have three independent components, but are treated in exactly the same way as in the two dimensional case. The position of an object is now described by three independent functions, x(t), y(t), z(t).

- 4.4: Circular motion
- We often consider the motion of an object around a circle of fixed radius, R . In principle, this is motion in two dimensions, as a circle is necessarily in a two dimensional plane. However, since the object is constrained to move along the circumference of the circle, it can be thought of (and treated as) motion along a one dimensional axis that is curved.