Scalars and Vectors
With forces direction is important so force is a vector quantity.
Time has no direction so it is a scalar quantity.
Scalar – magnitude (size) only
Vector – magnitude
- direction
- reference point
eg distance, d = 34 km
eg. Displacement, s = 34 km
south
of Edinburgh
quantity
symbol
unit
symbol
Scalar
vector
d
metre
Displacement
s
metre
m
v
Speed
v
Metres per
second
m/s or ms-1
s
Velocity
v
Metres per
second
m/s or ms-1
v
Metres per
second per sec
Acceleration
s
or
Time
F
newtons
Energy
J
m
kilogram
kg
quantity
symbol
unit
symbol
Scalar
vector
Distance
d
metre
m
s
Displacement
s
metre
m
v
Speed
v
Metres per
second
m/s or ms-1
s
Velocity
v
Metres per
second
m/s or ms-1
v
Acceleration
a
Metres per
second per sec
m/s2 or ms-2
v
Time
t
second
s
s
Force
F
newtons
N
v
Energy
E
joules
J
s
Mass
m
kilogram
kg
s
Directions
Left/right, up/down
30o above horizontal
North, south etc
3 figure bearings 315o north west
N orth
000°
010°
020°
030°
N orth W est 3 1 5 °
N orth E a st 0 4 5 °
060°
070°
080°
E ast 0 9 0 °
W est 2 7 0 °
100°
11 0 °
120°
Sou th W est 2 2 5 °
Sou th E ast 1 3 5 °
150°
200°
160°
1 9 0 ° Sou th 1 7 0 °
180°
Example
Draw a scale diagram to find the distance travelled and the
final displacement of someone following this route.
4 km at 045o
N
2 km due south
Scale 1cm: 1km
6 km at 60o south of east
resultant
Now do the extra
example sheet
Distance = 12 km
Displacement = 7.4 km at 128o
Distance = 12 km
Displacement = 7.4 km at 128o
(a) If a boy took 4 hours to complete this course, what was his
average speed in km/hour?
(b) What was his average velocity?
(c) What was his velocity in m/s?
Average speed = d ÷ t = 12 ÷ 4 = 3 km/h
( b) average velocity = s ÷ t = 7.4 ÷ 4 = 1.85 km/h
At 128o
(c) 1.85 km/h = 1850 m/h = 30.83 m/min = 0.51 m/s at 128o
Now do tutorial questions 14, 15
2010 Higher paper Qu 21
A helicopter is flying at a constant height above the ground.
(a) The helicopter flies 20km on a bearing of 180o (due south). It
then turns on to a bearing of 140o and travels a further 30km.
The helicopter takes 15 minutes to travel the 50km.
(i) By scale diagram or otherwise find the resultant displacement of
the helicopter.
(2)
(ii) Calculate the average velocity of the helicopter during the 15
minutes.
(2)
Examples: Find the resultant vector (add vectors nose to tail.)
(a)
65 N
140 N
For forces the resultant vector is
called the unbalanced force.
(b)
10 N
30o
30o
10 N
Now do tutorial questions 16 to
22 ( you might need a hint with
Qu 19)
Example: Resolve the forces on this garden roller to find the
horizontal force on it.
100 N
60o
Now try tutorial questions 23 to 26
Scalars and Vector Review
Make sure you complete all the following.
Tutorial Questions 14 to 26
SAQ 1 to 16
Homework 3
Purple book 1.1 except Qu 2,3