 | | If we were points confined to a straight line along a single coordinate axis, then distance and speed might suffice to describe all possibilities and there would be no need for vectors. Fortunately, the universe is three dimensional and much more interesting. Vectors are a fundamental part of the language of physics because they allow us to describe three-dimensional behavior. This chapter describes how to use vectors, add and subtract vectors, and solve problems with vectors. Position and displacement are vectors that describe location and changes in location. Velocity and acceleration vectors describe motion. The force vector describes the three-dimensional character of forces. Vectors are useful in solving many real-world problems, such as projectile motion of a soccer ball kicked through the air, motion of a car rolling down a ramp, and control of a robot maneuvering through a maze. |  | | By the end of this chapter you should be able to
|  | find the magnitude and components of a force, displacement, velocity, or acceleration vector;
| | represent and perform calculations with force, displacement, velocity, or acceleration vectors in Cartesian and polar forms;
| | convert between Cartesian and polar vectors;
| | find the resultant of two or more vectors both graphically and by components;
| | apply the technique of breaking down a two- or three-dimensional problem into separate one-dimensional problems; and
| | solve two-dimensional motion problems, including projectile motion and motion down a ramp.
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|  | 6A: Vector navigation
6B: Projectile motion
6C: Acceleration on an inclined plane
6D: Graphing motion on an inclined plane |
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