Base units and vectors Units and prefixes Prefix Symbol Multiple
of unit
Base One from which all other (10n)
unit units can be derived Base Symbol SI (International
quantity System) unit Femto f 10-15
Derived One made up from a
unit combination of two or more Length l metre (m) Pico p 10-12
base units Mass m kilogram (kg) Nano n 10-9
Scalar A quantity fully described by Time t second (s) Micro μ 10-6
a magnitude (numerical
value) alone Electric I ampere (A) Milli m 10-3
current
Vector A quantity fully described by Centi c 10-2
both a magnitude and Temperature T kelvin (K)
specified direction Kilo k 103
Amount of n (mol) mole (mol)
Physical Anything measurable with a substance Mega M 106
quantity numerical magnitude and unit Giga G 109
SI units (N, J, C, V, W, All equations are
Vector and scalar Ω) can be derived from
these base units
homogenous; same
units and magnitude
Tera T 1012
quantities Scalars change
with magnitude:
F = ma = kgms-2 on both sides Unit prefixes are used to convert
There are six vector
quantities:
●
distance (m) Constants, e.g. π, are
ignored
Combining between units by multiplying -
400nm = 400x10-9m
●
displacement (m)
●
●
speed (ms-1)
time (s) Join vectors head to
vectors For exponentiated units, prefix
●
velocity (ms-1)
●
acceleration (ms-2)
●
power (W) tail; next one starts Resultant vector is one also included
●
force (N)
●
energy (J) where previous ends. gained from adding two e.g. Tm3 = Tm x Tm x Tm = 1036m3
or more vectors
weight (N) KE scalar as
Components of
●
together.
●
momentum (kgms-1) squaring velocity θ
means loss of
α
Magnitude found vectors
R
directional info
Waves using a2 + b2 = c2
es
(always +ve) Vertical component: vx
u
lta
= vsinθ v
nt
Direction found using
Wave Disturbance which
R(
trigonometry e.g. 45° Horizontal component:
)
propagates through a
to horizontal / vertical vx = vcosθ
medium, carrying energy θ
Answers are rounded to the same number of
Types of waves S.Fs as the least accurate measurement
Term Definition
e.g. 39 x 234 = 9100
Examples
...on a N
g = 9.81ms-2
Progressive / Transfer energy from one place to EM (light), sound
slope:
travelling another: don’t transfer material F
mgsinθ θ
Standing / Don’t transfer energy - stored within Vibrations in bass string,
stationary wave system sound in closed system θ W
mgcosθ
Mechanical Produced by disturbances in material Sound, water waves, waves Two cases: Friction is force
and transmit energy by oscillating in spring
θ that opposes
inθ
particles – can’t go through vacuum sin motion gs
mg m
ion
on ct
Electromagnetic Oscillating electric and magnetic fields. Light, radio, and cti Fri
Don’t need medium to transmit energy – microwaves Fri
can go through vacuum Moving down Moving up
Transverse Oscillation of particles perpendicular to
direction of energy transfer
Water and EM waves
Waves graphs
Transverse and longitudinal waves
Longitudinal Oscillation of particles parallel to Sound waves
direction of energy transfer graphed as transverse: properties
easier shown and determined. Two
Transverse Longitudinal graphs used:
y x
Cycle Displacement of particles •
Displacement vs. Distance –
particles’ displacement at fixed
Wavelength λ / Rarefaction Compression instant in time
Displacement of particles
Time period t •
Displacement vs. Time – variation
Wavelength in a particle’s position with time
Crest Energy + +
displacement
of wave
Displacement of particles
Distance
travelled by
Trough wave / time
Undisturbed
/ equilibrium Energy + displacement of wave Wavelength λ /
Amplitude
position Time period t
-
, Wave properties Wave
eqns:
v = fλ
ms-1 = Hz x m
T = f-1
T = s-1
Phase ...is a description of the point in a wave’s
cycle, where one wavelength or time period equals 360o
Property Definition or 2π radians.
A + D in phase (0o difference):
+ same displacement, same direction
Displacement / m Particle’s distance from equilibrium position
B
Amplitude / m Maximum displacement from equilibrium position
Displacement
of particles
Time / distance
90o 180o 270o 360o
Period / s Time taken for one complete oscillation
A
D
Frequency / Hz Number of complete waves passing a single B + C in
point in a second antiphase: 180o C
-
out of phase
Wavelength / m Distance between consecutive points of
corresponding phase e.g. two crests Waves of equal f and λ are comparable – phase
difference is fraction of a cycle by which a wave leads
Wave speed / ms-1 Distance travelled by wave per second or lags the other
Polarisation ...is a process leading to waves becoming
A ahead of B; further in
oscillation cycle. Phase
polarised; having oscillations confined to a single plane difference is 90o or ½π r.
perpendicular to direction of wave travel. Occurs only on transverse Phase difference is 180o;
waves and can identify them; longitudinal waves are non-polarised. half a cycle out of phase
e.g. light from a lamp is unpolarised; propagating waves have / antiphase
oscillations in all planes perpendicular to direction of wave travel No difference; in phase /
same point in wave cycle
Vertical
Max. Distance / Motion
displacement ...is distance
from a fixed point in a specified
direction. Velocity is rate of change of
0 displacement.
Horizontal
Distance is length between two points,
and speed rate of change of distance
An analyser – sheet of Polaroid – verifies if
wave is polarised: wave passes through Constant distance; Constant velocity;
As light passes through polarisation and analyser is rotated through 360o, no velocity no acceleration
filter / polariser, oscillations occur in polarising wave into a single plane.
single plane. Polariser can be rotated to
polarise source into any perpendicular Constant intensity throughout rotation
plane. means unpolarised source; oscillations in io n
multiple planes pass through. le ra t
If light passed through another vertical D ece
Distance
polariser, nothing would occur – already Intensity varying between 0 and a max on
polarised in that plane. With a r at i
TWICE throughout rotation means polarised ele
perpendicular polariser, i.e. horizontal, c
source: only passes when analyser parallel Ac
no light passes as only waves oscillating with source’s plane of polarisation and Time
in horizontal direction can pass; 2 blocked as analyser rotated. More distance covered per unit time → non-
polarisers needed to cancel out a wave. uniform velocity → acceleration. Gradient of two
points on curve is equal to the average velocity
Region of Typical Applications Electromagnetic during that time, and gradient of tangent is the
instantaneous velocity
short λ, high f
spectrum λ/m
• Sterilising medical
radiation EM waves In displacement-time graph, total distance
is sum of journeys
Gamma equipment cover a range of wavelengths
10-16 - 10-12 called the EM spectrum. While
rays • Medical imaging For object projected upwards
Displacement
• Killing cancerous cells continuous, wavelength variation
results in different properties
Cause ionisation
Distance
• Airport security scanners
• Medical imaging (broken along spectrum, meaning it is
X-rays 10 -12
- 10 -9
bones) divisible into regions, and these
• Studying crystal structures overlap – no specific boundaries
• Vitamin D production in Time Time
body Waves in EM spectrum all have
Ultraviolet
light
10-9 - 10-7
•
•
Sun beds
Causes fluorescence in
some common properties: Acceleration is rate of
security marking and
●
Transverse change of velocity with time, and
detects counterfeit notes
V ●
Can propagate through a can be either:
I vacuum Uniform
4 x 10-7 – • Photosynthesis B ●
Travel at a speed of 3.00 x 108
7 x 10-7 • Photography G
Visible light ms-1
400nm – • Vision
Velocity
700nm Y
O
Gravity g = 9.81ms-2
Cause heating
• Cooking, grilling R
Infrared 10-6 - 10-4 • Remote controls
• Thermal imaging devices Time
v=0 u=0 Non-uniform
long λ, low f
Microwave
• Cooking a = -9.81 a = -9.81 n No acceleration
io
10-4 - 10-1 Mobile phones rat
•
s e
• Satellite communications cel
Ac De
Velocity
ce lera
• Radio / television
Radio t i on
waves
10 - 10
-1 5
communications Time up = time down
• Radio astronomy
Time
, Constant acceleration Velocity-time graph For a velocity-time graph, area under the
graph BETWEEN SPECIFIED POINTS,
Average velocity is change in position where area above the x-axis is positive
Constant velocity: u – initial velocity
divided by the time of travel. and below negative, gives displacement
s = vt v – final velocity
a - acceleration Object thrown One bounce
s – distance Constant velocity; Constant
Constant acceleration: no acceleration acceleration
upwards
v = u + at travelled
s = ut + ½at2 t – time taken
Velocity
Velocity
avg. velocity = (v + u)/2
v2 = u2 + 2as Time Time
Graphing
Velocity
Vertical distance
between first plotted point and last must Time
occupy at least half the height (i.e. 7
squares) as should horizontal distance half PP 1 – measurement
the width (i.e. 4.5 squares). Non-uniform acceleration. Gradient of two
points on curve is equal to the average
of acceleration due
Gradient triangle must be large, well over acceleration during that time, and gradient of
tangent is the instantaneous acceleration to gravity
half line’s length, to remove gradient
measurement errors Apparatus:
Method: ●
Two light gates – reduce human error
1) Set up apparatus with light gates
Projectile motion ...has connected to timing unit set to
●
Timing unit and suitable power
supply
constant acceleration in one direction, and measure time. ●
Piece of card weighted at one end
no acceleration in perpendicular direction 2) Measure and record vertical ●
Retort stand and two bosses
distance between detectors of two ●
Metre rule
Projectiles ...are objects upon light gates (centre) with metre rule –
height fallen by card
●
Leads
which the only acting force is gravity.
3) Hold weighted card with heavy end Analysis and conclusions:
Projectiles Parabola Not at rest; lowest slightly above top light gate – Always use mapping to find a given
follow a horizontal
parabolic component
from rest (u = 0) – and drop so it relationship (variable) and plot y =
path cuts through light beams of both mx + c, especially if given formula. In
light gates; release card carefully so this case:
Height
Same height = same velocity it always falls vertically s = ut + ½at2
4) Record time taken to pass through h = ½at2
light gate and repeat measurement y = mx
three times to work out an average
Range (reliability) Results in straight line graph passing
5) Repeat (reliability), varying the through origin when plotting h against
Projectile’s overall motion is result of height between light gates. Take at t2, and g is 2 × gradient
horizontal and vertical motion, and these least 6 readings with as wide a
range as possible. c (y-intercept) must be a constant in
are considered separately. experiment, so controlled variables
Measurements only as accurate as ensure it does not change
Time is same horizontally and vertically, instruments, and calculated values
and is twice time to reach highest point Always specify measuring
have same s.f. as values – no extra instruments and the variable you
accuracy repeat and average. Units in table
Horizontal ...velocity Vertical Particle
is constant; a is 0. stops in vertical same as instruments’ units.
Errors (always there, not a mistake):
Only S = D/T used. direction at highest ●
Parallax error – looking at analogue
point, and starts scale at an angle Weighted card
Range = Horizontal
from rest when ●
Difficult to know exact centre of gate
velocity x Time of
released from it. ●
Timing may not start when u = 0 Light gates
flight
●
Uncertainty of 1mm as the smallest On
Refraction reading you can make on the
Height
instrument (ruler) in the units you are
Timer
recording in. If both ends were not
Refraction Change in direction of a
fixed, this would be 2mm. Also 0.01s
wave travelling between Off
on light gate
different media caused by
its change in speed When light enters medium
Retraceable: putting normal to surface (i = 0), entire
Normal
Incident One which strikes boundary
ray between two different media Crest In c ray through refracted ray slows down at same time:
id e gives incident no refraction occurs. If it strikes
nt
ra y surface at an angle, some of ray
Refracted One which has entered λ ra y strikes before rest, so some
ray second medium and c ted n
e
efl
w slowed down before rest,
changed direction i r kr
dra
lly
a ua leading to bending
We No
t us
Critical Angle of incidence
angle producing an angle of Air – less optically dense Label boundary / interface
refraction of 90o Glass – more optically dense
Re
Refractive Ratio of the speed of a ray i = r, both measured
fr
a ct
index of light when passing from between normal and
ed
one medium into another ray
Light bends towards normal
ra y
Normal Line perpendicular to the v = fλ – f constant, v travelling into more optically
boundary and λ proportional dense material, and away into
less optically dense
of unit
Base One from which all other (10n)
unit units can be derived Base Symbol SI (International
quantity System) unit Femto f 10-15
Derived One made up from a
unit combination of two or more Length l metre (m) Pico p 10-12
base units Mass m kilogram (kg) Nano n 10-9
Scalar A quantity fully described by Time t second (s) Micro μ 10-6
a magnitude (numerical
value) alone Electric I ampere (A) Milli m 10-3
current
Vector A quantity fully described by Centi c 10-2
both a magnitude and Temperature T kelvin (K)
specified direction Kilo k 103
Amount of n (mol) mole (mol)
Physical Anything measurable with a substance Mega M 106
quantity numerical magnitude and unit Giga G 109
SI units (N, J, C, V, W, All equations are
Vector and scalar Ω) can be derived from
these base units
homogenous; same
units and magnitude
Tera T 1012
quantities Scalars change
with magnitude:
F = ma = kgms-2 on both sides Unit prefixes are used to convert
There are six vector
quantities:
●
distance (m) Constants, e.g. π, are
ignored
Combining between units by multiplying -
400nm = 400x10-9m
●
displacement (m)
●
●
speed (ms-1)
time (s) Join vectors head to
vectors For exponentiated units, prefix
●
velocity (ms-1)
●
acceleration (ms-2)
●
power (W) tail; next one starts Resultant vector is one also included
●
force (N)
●
energy (J) where previous ends. gained from adding two e.g. Tm3 = Tm x Tm x Tm = 1036m3
or more vectors
weight (N) KE scalar as
Components of
●
together.
●
momentum (kgms-1) squaring velocity θ
means loss of
α
Magnitude found vectors
R
directional info
Waves using a2 + b2 = c2
es
(always +ve) Vertical component: vx
u
lta
= vsinθ v
nt
Direction found using
Wave Disturbance which
R(
trigonometry e.g. 45° Horizontal component:
)
propagates through a
to horizontal / vertical vx = vcosθ
medium, carrying energy θ
Answers are rounded to the same number of
Types of waves S.Fs as the least accurate measurement
Term Definition
e.g. 39 x 234 = 9100
Examples
...on a N
g = 9.81ms-2
Progressive / Transfer energy from one place to EM (light), sound
slope:
travelling another: don’t transfer material F
mgsinθ θ
Standing / Don’t transfer energy - stored within Vibrations in bass string,
stationary wave system sound in closed system θ W
mgcosθ
Mechanical Produced by disturbances in material Sound, water waves, waves Two cases: Friction is force
and transmit energy by oscillating in spring
θ that opposes
inθ
particles – can’t go through vacuum sin motion gs
mg m
ion
on ct
Electromagnetic Oscillating electric and magnetic fields. Light, radio, and cti Fri
Don’t need medium to transmit energy – microwaves Fri
can go through vacuum Moving down Moving up
Transverse Oscillation of particles perpendicular to
direction of energy transfer
Water and EM waves
Waves graphs
Transverse and longitudinal waves
Longitudinal Oscillation of particles parallel to Sound waves
direction of energy transfer graphed as transverse: properties
easier shown and determined. Two
Transverse Longitudinal graphs used:
y x
Cycle Displacement of particles •
Displacement vs. Distance –
particles’ displacement at fixed
Wavelength λ / Rarefaction Compression instant in time
Displacement of particles
Time period t •
Displacement vs. Time – variation
Wavelength in a particle’s position with time
Crest Energy + +
displacement
of wave
Displacement of particles
Distance
travelled by
Trough wave / time
Undisturbed
/ equilibrium Energy + displacement of wave Wavelength λ /
Amplitude
position Time period t
-
, Wave properties Wave
eqns:
v = fλ
ms-1 = Hz x m
T = f-1
T = s-1
Phase ...is a description of the point in a wave’s
cycle, where one wavelength or time period equals 360o
Property Definition or 2π radians.
A + D in phase (0o difference):
+ same displacement, same direction
Displacement / m Particle’s distance from equilibrium position
B
Amplitude / m Maximum displacement from equilibrium position
Displacement
of particles
Time / distance
90o 180o 270o 360o
Period / s Time taken for one complete oscillation
A
D
Frequency / Hz Number of complete waves passing a single B + C in
point in a second antiphase: 180o C
-
out of phase
Wavelength / m Distance between consecutive points of
corresponding phase e.g. two crests Waves of equal f and λ are comparable – phase
difference is fraction of a cycle by which a wave leads
Wave speed / ms-1 Distance travelled by wave per second or lags the other
Polarisation ...is a process leading to waves becoming
A ahead of B; further in
oscillation cycle. Phase
polarised; having oscillations confined to a single plane difference is 90o or ½π r.
perpendicular to direction of wave travel. Occurs only on transverse Phase difference is 180o;
waves and can identify them; longitudinal waves are non-polarised. half a cycle out of phase
e.g. light from a lamp is unpolarised; propagating waves have / antiphase
oscillations in all planes perpendicular to direction of wave travel No difference; in phase /
same point in wave cycle
Vertical
Max. Distance / Motion
displacement ...is distance
from a fixed point in a specified
direction. Velocity is rate of change of
0 displacement.
Horizontal
Distance is length between two points,
and speed rate of change of distance
An analyser – sheet of Polaroid – verifies if
wave is polarised: wave passes through Constant distance; Constant velocity;
As light passes through polarisation and analyser is rotated through 360o, no velocity no acceleration
filter / polariser, oscillations occur in polarising wave into a single plane.
single plane. Polariser can be rotated to
polarise source into any perpendicular Constant intensity throughout rotation
plane. means unpolarised source; oscillations in io n
multiple planes pass through. le ra t
If light passed through another vertical D ece
Distance
polariser, nothing would occur – already Intensity varying between 0 and a max on
polarised in that plane. With a r at i
TWICE throughout rotation means polarised ele
perpendicular polariser, i.e. horizontal, c
source: only passes when analyser parallel Ac
no light passes as only waves oscillating with source’s plane of polarisation and Time
in horizontal direction can pass; 2 blocked as analyser rotated. More distance covered per unit time → non-
polarisers needed to cancel out a wave. uniform velocity → acceleration. Gradient of two
points on curve is equal to the average velocity
Region of Typical Applications Electromagnetic during that time, and gradient of tangent is the
instantaneous velocity
short λ, high f
spectrum λ/m
• Sterilising medical
radiation EM waves In displacement-time graph, total distance
is sum of journeys
Gamma equipment cover a range of wavelengths
10-16 - 10-12 called the EM spectrum. While
rays • Medical imaging For object projected upwards
Displacement
• Killing cancerous cells continuous, wavelength variation
results in different properties
Cause ionisation
Distance
• Airport security scanners
• Medical imaging (broken along spectrum, meaning it is
X-rays 10 -12
- 10 -9
bones) divisible into regions, and these
• Studying crystal structures overlap – no specific boundaries
• Vitamin D production in Time Time
body Waves in EM spectrum all have
Ultraviolet
light
10-9 - 10-7
•
•
Sun beds
Causes fluorescence in
some common properties: Acceleration is rate of
security marking and
●
Transverse change of velocity with time, and
detects counterfeit notes
V ●
Can propagate through a can be either:
I vacuum Uniform
4 x 10-7 – • Photosynthesis B ●
Travel at a speed of 3.00 x 108
7 x 10-7 • Photography G
Visible light ms-1
400nm – • Vision
Velocity
700nm Y
O
Gravity g = 9.81ms-2
Cause heating
• Cooking, grilling R
Infrared 10-6 - 10-4 • Remote controls
• Thermal imaging devices Time
v=0 u=0 Non-uniform
long λ, low f
Microwave
• Cooking a = -9.81 a = -9.81 n No acceleration
io
10-4 - 10-1 Mobile phones rat
•
s e
• Satellite communications cel
Ac De
Velocity
ce lera
• Radio / television
Radio t i on
waves
10 - 10
-1 5
communications Time up = time down
• Radio astronomy
Time
, Constant acceleration Velocity-time graph For a velocity-time graph, area under the
graph BETWEEN SPECIFIED POINTS,
Average velocity is change in position where area above the x-axis is positive
Constant velocity: u – initial velocity
divided by the time of travel. and below negative, gives displacement
s = vt v – final velocity
a - acceleration Object thrown One bounce
s – distance Constant velocity; Constant
Constant acceleration: no acceleration acceleration
upwards
v = u + at travelled
s = ut + ½at2 t – time taken
Velocity
Velocity
avg. velocity = (v + u)/2
v2 = u2 + 2as Time Time
Graphing
Velocity
Vertical distance
between first plotted point and last must Time
occupy at least half the height (i.e. 7
squares) as should horizontal distance half PP 1 – measurement
the width (i.e. 4.5 squares). Non-uniform acceleration. Gradient of two
points on curve is equal to the average
of acceleration due
Gradient triangle must be large, well over acceleration during that time, and gradient of
tangent is the instantaneous acceleration to gravity
half line’s length, to remove gradient
measurement errors Apparatus:
Method: ●
Two light gates – reduce human error
1) Set up apparatus with light gates
Projectile motion ...has connected to timing unit set to
●
Timing unit and suitable power
supply
constant acceleration in one direction, and measure time. ●
Piece of card weighted at one end
no acceleration in perpendicular direction 2) Measure and record vertical ●
Retort stand and two bosses
distance between detectors of two ●
Metre rule
Projectiles ...are objects upon light gates (centre) with metre rule –
height fallen by card
●
Leads
which the only acting force is gravity.
3) Hold weighted card with heavy end Analysis and conclusions:
Projectiles Parabola Not at rest; lowest slightly above top light gate – Always use mapping to find a given
follow a horizontal
parabolic component
from rest (u = 0) – and drop so it relationship (variable) and plot y =
path cuts through light beams of both mx + c, especially if given formula. In
light gates; release card carefully so this case:
Height
Same height = same velocity it always falls vertically s = ut + ½at2
4) Record time taken to pass through h = ½at2
light gate and repeat measurement y = mx
three times to work out an average
Range (reliability) Results in straight line graph passing
5) Repeat (reliability), varying the through origin when plotting h against
Projectile’s overall motion is result of height between light gates. Take at t2, and g is 2 × gradient
horizontal and vertical motion, and these least 6 readings with as wide a
range as possible. c (y-intercept) must be a constant in
are considered separately. experiment, so controlled variables
Measurements only as accurate as ensure it does not change
Time is same horizontally and vertically, instruments, and calculated values
and is twice time to reach highest point Always specify measuring
have same s.f. as values – no extra instruments and the variable you
accuracy repeat and average. Units in table
Horizontal ...velocity Vertical Particle
is constant; a is 0. stops in vertical same as instruments’ units.
Errors (always there, not a mistake):
Only S = D/T used. direction at highest ●
Parallax error – looking at analogue
point, and starts scale at an angle Weighted card
Range = Horizontal
from rest when ●
Difficult to know exact centre of gate
velocity x Time of
released from it. ●
Timing may not start when u = 0 Light gates
flight
●
Uncertainty of 1mm as the smallest On
Refraction reading you can make on the
Height
instrument (ruler) in the units you are
Timer
recording in. If both ends were not
Refraction Change in direction of a
fixed, this would be 2mm. Also 0.01s
wave travelling between Off
on light gate
different media caused by
its change in speed When light enters medium
Retraceable: putting normal to surface (i = 0), entire
Normal
Incident One which strikes boundary
ray between two different media Crest In c ray through refracted ray slows down at same time:
id e gives incident no refraction occurs. If it strikes
nt
ra y surface at an angle, some of ray
Refracted One which has entered λ ra y strikes before rest, so some
ray second medium and c ted n
e
efl
w slowed down before rest,
changed direction i r kr
dra
lly
a ua leading to bending
We No
t us
Critical Angle of incidence
angle producing an angle of Air – less optically dense Label boundary / interface
refraction of 90o Glass – more optically dense
Re
Refractive Ratio of the speed of a ray i = r, both measured
fr
a ct
index of light when passing from between normal and
ed
one medium into another ray
Light bends towards normal
ra y
Normal Line perpendicular to the v = fλ – f constant, v travelling into more optically
boundary and λ proportional dense material, and away into
less optically dense
