Units & Equations Page

Here is a list of important S.I. units of Physical Quantities used in Physics for ordinary level examinations (first examinations)

A sound knowledge of these units is a first step towards success in examinations.

I advise Physics students to revise these units at least once per week.

UNITS

Note: Those units marked with an asterisk (*) are only required by the Matsec

Syllabus. All the rest are included both in the University of London and in the

Matsec syllabus.

Note:

Matsec stands for Matriculation Certificate in Secondary Education which is set by the University of Malta Examinations Board. The G.C.E. London is set by the University of London (United Kingdom) Examinations and Assessment Council.

Physical Quantity
Unit used
Symbol
1. Force
newton
N
2. Weight
newton
N
3. Mass
kilogram
kg
4. Moment of a force
newton metre
N m
5. Average speed
metre per second
m / s
6. Acceleration
metre per second squared
m / s2
7. Velocity
metre per second

(in a given direction)
m / s

+ direction
8. Momentum
kilogram metre per second
kg. m / s
9. Work
joule
J
10. Power
watt
W
11. Energy (all forms)
joule
J
12. Efficiency
no units
-
13. Temperature
kelvin
K
14. Specific heat capacity
joule per kilogram kelvin
J / (kg.K)
15. Density
kilogram per metre cubed
kg / m3
16. Pressure
newton per square metre

or Pascal
N / m2

or Pa
17. Electric Current
Ampere
A
18. Electric Charge
Coulomb
C
19. Voltage

or potential difference

Volt
V
20. Capacitance *
farad
F
21. Resistance
ohm
W
22. Commercial unit of

electrical energy

kilowatt hour
kWh
23. Refractive index
no units
-

EQUATIONS

Physical Quantities involved
Equation

(or relationship)
Notes
1. Moment of a force Moment of a force about a given point

= Force x perpendicular distance from line of action of force to point

-
2. Unbalanced force (F)
F = m . a

(N) = (kg) . ( m / s 2 )
F = unbalanced force

m = mass

a = acceleration

3. Weight of a body, expressed in newtons
W = m . g

( N ) = (kg) . (m / s2)
W = weight

g = acceleration due to gravity

4. Average speed average speed = total distance moved / time
-
5. Average velocity average velocity = total displacement / time displacement = distance + direction
6. Acceleration acceleration = change in velocity / time

= ( final velocity - initial velocity) / time

-
7. D-t graphs The gradient (or slope) of a D-t graph represents the speed or velocity
-
8. V-t graphs i) The slope or gradient of a V-t graph represents the acceleration

(ii) The area under a V-t graph ( i.e. the area enclosed between the graph and the time axis) represents the distance or displacement covered in a particular time.

-
9. Momentum
momentum = mass x velcoity

( kg.m / s ) = (kg) (m/s)
N.B. direction has to be indicated if given
10. Equations of motion with uniform acceleration (i) v = u + a . t

(ii) s = ½ a . t2 used when u = 0 (or object starts moving from rest)

(iii) s = ( u + v) /2 . t

where:

v = final velocity

8 = initial velocity

a = acceleration

t = time

s = distance moved

Note: a is negative for retardation

11. Work (or energy converted) Work = Force x distance moved (in direction of force) Work in joules if force in newtons and distance in metres
12. Power (or rate of energy conversion) Power = work done / time taken

= energy converted / time

power in watts if work or energy in joules and time in seconds
13. Gravitational potential energy G.P.E. = m . g . h

(J) = (kg) . (m/s2) . m

Note: h MUST BE IN METRES
14. Kinetic energy K.E. = ½ m . v2 K.E. in joules if m in kg and v in m/s
15. Power Power = ( force x distance) / time

or power = force x velocity

Not very common
16. Efficiency of machines (%) efficiency =

( useful work output / total work input) x 100

= work done on load / work done by effort x 100

In a practical machine the efficiency is less than 100% due to energy losses like heat in overcoming frictional forces
17. Work output work output = load x distance moved by load -
18. Work input work input = effort x distance moved by effort -
19. Wasted work work wasted = (work input) minus (work output) -
20. Conversion of temperature from Celsius scale to Kelvin Scale and vice-versa
(temp.) in oC + 273 = temp. in Kelvin

temp. in Kelvin - 273 = temp. in Celsius
e.g.

37oC = 37 + 273

= 310 K

21. Specific heat capacity and quantity of heat energy absorbed or given out
Q = m . c. Dq
where

Q = quantity of heat given out or absorbed,

m = mass

c = sp. Heat capacity,

D q

=temperature

difference

22. Density (r)
density = mass / volume
23. Pressure (p)
pressure = Force / Area
force acts at right angles to the area over which it acts

If force is in N and area in m2, then pressure is in Pascals

24. Pressure in a fluid
p = h. r . g
h = vertical height
25. Pressure Law
p1 / T 1 = p2 / T 2

London only
T must be in kelvin

volume constant

26. Charles' Law
V 1 / T 1 = V 2 / T 2

London only
pressure constant
27. Boyle's Law
p1 . V 1 = p 2 . V 2

London only
temperature constant
28. Electric charge (Q)
Q = I . t
t must be in seconds, for Q to be in coulombs
29. Electric energy a) Energy = V . Q

b) Energy = V . I . t

c) Energy = I 2 . R. t

where

V = p.d. in volots

I = current in amps

R = resistance in ohms

t = time in seconds

energy = in joules

30. Electric power a) p = V . I

b) p = I 2 . R

c) p = V 2 / R

31. Capacitance (C)
C = Q / C or Q = C . V
Matsec only
32. Ohm's Law
V = I . R
I = current

V = p.d. or voltage

R = resistance

33. Adding resistors in series
R T = R 1 + R 2 + R 3 + ……….
33. Adding resistors in parallel General Equation (for any number of resistors)

1 / RT = 1 / R 1 + 1 / R 2 + 1 / R 3 etc

Special Case of 2 resistors in parallel

R T = (R 1 x R 2) / (R 1 + R 2)

Note: In Matsec syllabus only 2 resistors will be given connected in parallel

where R T represents the total or effective resistance
34. How current sub-divides in a parallel pair of resistors Let current through R 1 be i 1 and let that through R2 be i 2

then,

i 1 = I ( R 2 ) / ( R 1 + R 2)

and

1 2 = I ( R 1 ) / ( R 1 + R 2)

I = total current entering the junction of the 2 resistors in parallel
35. Commercial unit of electrical energy - the kWh no. of kwh = (no. of watts) / 100 x (no. of h)

or

no. of kWh = (no. of kW) x no. of hours

36. C. R. O no. of complete cycles seen on screen

= input (signal) frequency across Y-plates/ time-base frequency (across X-plates)

37. Periodic Time (T) or period T = 1 / f where f = frequency
38. Induced e.m.f.

(Faraday's Law)

size of induced e.m.f. change in flux / time
39. Transformer equations a) Turns ratio equation:

n p / n s = v p / v s

b) Ideal transformer (= 100% efficient)

V p x I p = V s x I s

c) Efficiency of a transformer

(%) efficiency = power output (in secondary) / power input (in primary) x 100

40. Refractive index a) Refractive index for a ray of light travelling from air into a medium

= sine angle of incidence in air / sine angle of refraction in the medium

b) ref. Index = real depth / apparent depth

c) ref. Index = 1 / sine c (critical angle)

d) ref. Index = (velocity of light in air) / velocity of light in medium




In London exam. Only
42. magnification (m) m = height of image / height of object

or

m = image distance / object distance from lens

43. Wave equation
c or v = f . l

velocity = frequency x wavelength

44. Factors affecting frequency of vibration of a stretched wire a) f is directly proportional to 1 / l

b) f is directly proportional to root T

c) f is directly proportional to 1 / root m

where l = length of wire

T = tension of wire

m = mass per unit length or thickness

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