6.1 - vectors + scalars

between point A and B, which can fluctuate - distance or displacement?

distance

here

between point A and B, which is fixed - distance or displacement?

displacement

here

why does distance fluctuate?

• there are multiple routes to get from point to point

• abstractions, such as road closures, meaning a different route must be taken

here

why is displacement fixed?

because its the direct distance in a given direction (i..e, a straight line from point A to B) which doesn’t take into account routes or abstractions

what is displacement?

direct distance in a given direction

is displacement a vector or scalar quantity?

vector

is distance a vector or scalar quantity?

scalar

why is displacement a vector quantity?

it has a magnitude (distance) and direction

why is distance a scalar quantity?

it only has a magnitude

what is a vector?

any physical quantity that has a direction as well as a magnitude

what is a scalar?

any physical quantity that is not direction

what are examples of vector quantities?

• velocity

• acceleration

• force

• displacement

what are examples of scalar quantities?

• mass

• density

• energy

• distance

is velocity a vector or scalar quantity?

vector

why is velocity a vector quantity?

it has a magnitude (speed) and direction

is force a vector or scalar quantity?

vector

why is force a vector quantity?

it has a magnitude (force) and direction (denoted by positives and negatives)

is acceleration a vector or scalar quantity?

vector

how do we represent vectors?

• arrow

• arrow size = vector magnitude

• arrow direction = vector direction

what do arrows represent?

vectors

for vectors, what does arrow size represent?

the size (magnitude) of the vector

for vectors, what does arrow direction represent?

the direction of the vector

how do we represent the vector magnitude?

changing the size of the arrow proportionality

how do we represent the vector direction?

direction of arrow

what is velocity?

speed in a given direction

what is force?

• rate of change of momentum

• the product of the object’s mass and acceleration

what is acceleration?

rate of change of velocity

how can velocity be represented?

using arrows (vectors)

how can force be represented?

using arrows (vectors)

how can acceleration be represented?

using arrows (vectors)

AB = ?

OB - OA (b - a)

OB = ? (when you know AB and OA)

OB = OA + AB

where is the resultant force of this force diagram?

figure 4

here figure 4

what is a scale diagram?

here figure 4

how do you find the resultant force on a scale diagram?

here figure 4

what is the resultant?

combined effect

can you find the resultant of scalars or vectors?

vectors

which physical quantity can you find the resultant of - scalars or vectors?

vectors

how do you find the resultant when vectors are acting in the same direction?

adding them

here

how do you find the resultant when vectors are acting in opposite directions?

• if vectors are acting in completely opposite directions (180°), add them, with the direction of resolution marked

• if two vectors are perpendicular, use a right angled triangle and pythagoras’s theorem

• if two or more vectors aren’t perpendicular, find the horizontal and vertical components

how do you find the resultant when vectors are acting in completely opposite directions (180°)?

• assign the direction of resolution so you know which direction is positive

• add them

here

how do you find the resultant of two perpendicular vectors?

using phythagoras’s theorem (where the resultant is the hypotenuse)

here

how do you find the resultant of two or more vectors that aren’t perpendicular?

find the horizontal and vertical components

how do you find the bearing using the resultant displacement?

trig

here

what does it mean to resolve a vector into its perpendicular components?

to find the horizontal and vertical component of the angled vector using trig

here

how do you resolve a vector into its perpendicular components?

here

how do you find the horizontal component of a vector?

here

how do you find the vertical component of a vector?

here