Conceptual Physics

What is the displacement vector

if the car travels three times as

far?

su = (su,ș)

3 u = ( 3(50 km), 30º)

3 u = (150 km, 30º)

3.10 - Gotchas

Stating a value as a scalar when a vector is required. This happens in physics and everyday life as well. You need to use a vector when direction is required. Throwing a ball up is different than throwing a ball down; taking highway I-5 south is different than taking I-5 north. Vectors always start at the origin. No, they can start at any location.

3.11 - Summary

A scalar is a quantity, such as time, temperature, or speed, which indicates only amount. A vector is a quantity, like velocity or displacement, which has both magnitude and direction. Vectors are represented by arrows that indicate their direction. The arrow’s length is proportional to the vector’s magnitude. Vectors are represented withboldface symbols, and their magnitudes are represented with italic symbols. One way to represent a vector is with polar notation. The direction is indicated by the angle between the positive x axis and the vector (measured in the counterclockwise direction). For example, a vector pointing in the negative y direction would have a direction of 270° in polar notation. The magnitude is expressed separately. A polar vector is expressed in the form (r,ș) where r is the magnitude and ș is the direction angle. Another way to represent a vector is by using rectangular notation. The vector’sx and y components are expressed as an ordered pair of numbers (x,y). The components of a vector A are also written as Ax and Ay. To add vectors graphically, place the tail of one on the head of the other, then draw a vector that goes from the free tail to the free head: The new vector is the sum. To subtract, first take the opposite of the vector being subtracted, then add. (The opposite of a vector has the same magnitude, but it points in the opposite direction.)

Polar notation

v = (v,ș)

Rectangular notation

v = (vx,vy)

A + B = (Ax + Bx,Ay + By)