Chapter study guide

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.

6A: Vector navigation
6B: Projectile motion
6C: Acceleration on an inclined plane
6D: Graphing motion on an inclined plane

170Force vectors
171Resultant vector
173Finding component forces
174Adding and subtracting component vectors
175Finding magnitude and angle
176Net force and free-body diagrams
177Section 1 review
178Displacement, velocity, and acceleration
179Coordinate systems
1806A: Vector navigation
181Velocity vector
182Resolving component velocities
183Adding velocities
184Acceleration vector
185Section 2 review
186Projectile motion and inclined planes
187Equations of projectile motion
1886B: Projectile motion
189Graphing projectile motion
190Range of a projectile
191Solving projectile problems
1926C: Acceleration on an inclined plane
193Motion on an inclined plane
194Forces along a ramp
1956D: Graphing motion on an inclined plane
196Friction on an inclined plane
197Designing the Smart Cart
198Smart Cart measurements
199Section 3 review
200Chapter review
F =( F x , F y , F z )
F x =Fcosθ F y =Fsinθ
F= F x 2 + F y 2
θ= tan 1 ( F y F x )
a = Δ v Δt
x= v x0 t v x = v x0
y= v y0 t 1 2 g t 2 v y = v y0 gt
a ramp =( h L )g
a x =g(sinθ μ r cosθ)
vectorvector diagrammagnitudescalar
resultant vectorcomponent forcecomponentresolution of forces
sinecosinetangentradian (rad)
displacementpolar coordinatesCartesian coordinatescompass
projectilerangeinclined planeramp coordinates

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