# Motion in 2 and 3 dimensions

## The message for this week

In this material we try to set up an approach to motion in 2 dimensions. This makes use of vectors, and applies these concept to two concepts you have already met before coming here, the motion of projectiles and circular motion.

Please watch this video for a gentle introduction.

By the end of this week you should be able to solve problems for this type of motion using vectorial concepts, in all the following cases:

• Calculation of position and velocity
• Solve for projectile motion
• Calculate the details of circular motion:
• Both uniform
• and non-uniform
This material clearly depends on being able to solve 1-dimensional motion using calculus as discussed in this material and the "week 0" tutorial. It also make heavy use of vectors, for which we have additional support material.

## Next steps

We expect you to work your way through the online material, please feel free to ask questions on TEAMS and DISCUSSIONBOARD. After you have done that, but before Wednesday midnight, please try and answer as many of the questions on the MASTERINGPHYSICS test for this week. We shall discuss the results and the problems, as well as try and answer any remaining questions in the face-to-face session on FTFDAY. Only then should you attempt the tutorial sheets for this material.

## Guide through the material

We assume you have a basic understanding of calculus and its relation to linear kinematics. If you feel rusty, or are uncertain what we mean with this, please review the support material in the linear kinematics section.

In this section we combine these ideas with the use of vectors, into a full-fledged discussion of motion in 2 and 3 dimensions. We first look at the position and velocity as vectors, and in the next section we study acceleration.

We study two main applications: The motion of a projectile (such as the classical "cannon ball") under the influence of gravity, and the common problem (think of satellites orbiting the earth) of motion in a circle.