# Motion in Two and Three Dimensions

• Anders Malthe-Sørenssen
Chapter
Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

## Abstract

Newton’s second law is the main tool you need to solve problems in mechanics. However, so far, we have only addressed motion and forces in one dimension. Fortunately, the description of motion and Newton’s laws do not change when we go to higher dimensions. We can continue to apply the structured problem-solving approach in exactly the same way as we did before. But in order to address motion in two- and three dimensions, we need to extend our mathematical and numerical methods to address two- and three-dimensional motion. This will be done in two parts: In this chapter we introduce general two- and three-dimensional motion. Later we will introduce constrained motion—motion constrained to occur along a specific path in the same way a rollercoaster cart is constrained to follow the rollercoaster track, or in the way a part of a rotating body is following the rotation of the body.