Newton’s first law is only qualitative: we can’t use it calculate anything. 定性的

To go further, we need mathematical tools to describe motion: 3D vectors 矢量

3D coordinate system “Right-handed” 坐标系

A 3D vector is three numbers. Remember units! These are called the vector’s components. Blackboard

SI units [Length] [Mass] [Time] meters kilograms seconds m kg s Don’t forget to convert units!

A vector has a magnitude and a direction.

Magnitude: length of a vector If , then Magnitude is a scalar – just a number. 标量

Vectors can be made longer or shorter by multiplying with a scalar Vectors can be made longer or shorter by multiplying with a scalar. The direction will be reversed if the scalar is negative. The angle of the vector does not change.

Direction: the unit vector A unit vector has a magnitude of one, a points in some direction. How to calculate the unit vector in the direction of another vector: If , then Blackboard

Three special unit vectors is the unit vector along the x axis is the unit vector along the y axis is the unit vector along the z axis

Three special unit vectors Any vector can be written as a combination of these three unit vectors. Example:

Two vectors are equal if they have the same magnitude and direction.

Which of these vectors is equal to <-4,2,0>? b c d e

Vector addition 加法

Vector addition y x

Vector addition y x

Vector addition y x

Vector subtraction 减法

Vector subtraction y x

Vector subtraction y x

Vector subtraction y x

Which of the following statements are correct?

“final position - initial position” Displacement vectors 位移 A change in position, from position 1 to position 2, is given by: Greek letter “Delta” “final position - initial position”

Displacement vectors Example: A snail is initially at location r1 = <3,0,-7> m. Later the snail has crawled to r2 = <2,0,-8> m. What is Δr, the change in the snail’s position?