3.3 - Polar notation

Polar notation: Defining a vector by its angle

and magnitude.

Polar notation is a way to specify a vector. With polar notation, the magnitude and

direction of the vector are stated separately. Three kilometers due north is an example

of polar notation. “Three kilometers” is the magnitude and “north” is the direction. The

magnitude is always stated as a positive value. Instead of using “compass” or map

directions, physicists use angles. Rather than saying “three kilometers north,” a

physicist would likely say “three kilometers directed at 90 degrees.”

The angle is most conveniently measured by placing the vector’s starting point at the

origin. The angle is then typically measured from the positive side of the x axis to the

vector. This is shown in Concept 1 to the right.

Angles can be positive or negative. A positive angle indicates a counterclockwise

direction, a negative angle a clockwise direction. For example, 90° represents a quarter

turn counterclockwise from the positive x axis. In other words, a vector with a 90°

angle points straight up. We could also specify this angle as í270°.

The radian is another unit of measurement for angles that you may have seen before.

We will use degrees to specify angles unless we specifically note that we are using

radians. (Radians do prove essential at times.)

Polar notation

Magnitude and angle

Polar notation

v is magnitude

ș is angle

Writtenv = (v,ș)

Write the velocity vector of the

car in polar notation.

v = (v,ș)

v = (5 m/s, 135º)

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