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Forces
& Motion
Movement and Position: Displacement-Time and Velocity-Time Graphs ................................................... 2
Scalars and Vectors ................................................................................................................................... 2
Displacement (Distance) –Time ................................................................................................................ 2
Some problems ......................................................................................................................................... 6
Velocity-Time Graphs ................................................................................................................................ 7
Forces, Movement and Shape .................................................................................................................... 11
Addition of Forces, Balanced and Unbalanced Forces, Resultant Force ................................................ 11
Force, Mass and Acceleration ................................................................................................................. 12
Mass & Weight ........................................................................................................................................ 12
Terminal Velocity .................................................................................................................................... 14
Stopping Distances .................................................................................................................................. 15
Momentum ............................................................................................................................................. 15
Momentum and Force ........................................................................................................................ 16
Momentum, Collisions and Explosion................................................................................................. 18
Newton’s Laws of Motion ....................................................................................................................... 19
Moments – The Turning Effect of a Force .............................................................................................. 19
Centre of Gravity ..................................................................................................................................... 21
Stability and centre of gravity ............................................................................................................. 22
Forces on a light beam ............................................................................................................................ 23
Force-Extension Graphs .......................................................................................................................... 25
Hooke’s Law ............................................................................................................................................ 26
Astronomy................................................................................................................................................... 27
Moons ..................................................................................................................................................... 27
Gravitational Field Strength .................................................................................................................... 28
Gravity ..................................................................................................................................................... 28
Comets .................................................................................................................................................... 29
Orbital Speed, Orbital Radius and Time Period ...................................................................................... 29
Galaxies ................................................................................................................................................... 30
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Movement and Position: Displacement-Time and
Velocity-Time Graphs
Scalars and Vectors
Scalars are quantities like energy, power or speed. They have no direction. Vectors do have a direction.
Speed in a given direction is called velocity. Velocity is a vector, speed is not. Acceleration always has a
direction and hence is a vector as well. Distance is a scalar. Distance in a given direction is a vector and
called ‘displacement’.
Time seems to have a direction, but not in the three dimensions. The time cannot go ‘up’ or ‘left’, it is
therefore a scalar. The scientific definition of a vector is a ‘quantity that has magnitude and a direction’.
A scalar is a ‘quantity with magnitude, but no direction’.
Below is a list of vectors and scalars.
Scalars
Vectors
Energy
Acceleration
Power
Force
Voltage
Velocity
Current
Displacement
Time
Speed
distance
As vectors have a direction, they can be represented by arrows. The length of the arrow is proportional
to its magnitude.
Displacement (Distance) –Time
WARNING: In terms of language – non-physicists use the term distance most of
the time! This is OK !!! Although – when the direction counts, i.e. we talk about
objects moving forward and backwards or up and down then we need to use the
term displacement. The graphs below use displacement but with all bar one you
can replace that term easily with Distance. However, have a look at the last graph
in this section. It slopes downwards!!! Why ?
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The above graph shows an object which is not moving (at rest). Its displacement stays the same as time
goes by because it is not moving.
The above graph shows that the objects displacement increases as time goes by.
The object is moving and so it has velocity. The straight line shows it is a constant velocity.
The gradient (slope) of the line shows how fast the object is going.
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The above graph shows an object moving with constant velocity. Compare this with the graph on the
last one. and you will see that the slope is down rather than up. This means that the object is moving in
the opposite direction. As before, the slope of the line shows how fast the object is moving.
Speed is a measure of how fast an object is moving. It is measured in metres per second, written as m/s.
Speed = Distance ÷ Time.
In a formula speed and velocity are written as v:
v
d
t
This equation is important!
If an object is stationary (not moving), then its speed is zero.
Velocity is similar to speed. It is a measure of how fast an object is moving,
and is also measured in m/s.
Velocity = Displacement ÷ Time.
The difference between velocity and speed is that velocity is speed in a
certain direction. It is a vector quantity. If an object is moving in a straight
line,
then its speed and velocity will be the same. If the moving object stays at the
same speed but changes direction, then we say that the velocity has changed
(because the direction has changed) but the speed has stayed the same.
In most of the examples of motion that you will come across, the object will be moving in a straight line.
In this case, use the word velocity rather than speed.
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If an object moving in a straight line travels 25 metres in 5 seconds,
then its velocity = 25 ÷ 5 = 5 m/s.



You must always say what the units are! (in this case m/s, called "metres per second").
Always check what units are given in the question.
If the time is given in hours or minutes, then convert it to seconds before doing the calculation.
If an objects velocity does not change, we say it has a constant velocity.
In the above example, we are not told whether the object has a constant velocity, or whether its velocity
has changed during the 5 seconds. If the velocity has changed,
then the answer we have calculated is an average velocity of 5 m/s. If the velocity has not changed, then
the object had a constant velocity of 5 m/s.
When an objects velocity changes, it is called acceleration.
The curve in the above graph shows that an objects velocity is changing as time goes by. This is
acceleration.
Acceleration = Change in Velocity ÷ Time.
This equation is written as
a = (v-u) ÷ t
where a = acceleration, v = final velocity (the one it ended up with), u = initial velocity (the one it started
with), t = time
This equation is important!
The units of acceleration are m/s2 or ms-2, called "metres per second squared".
If an object gets faster, it will have a positive acceleration.
If an object gets slower, it will have a negative acceleration
(this is sometimes called "deceleration" but the term "negative acceleration" is preferred).
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Some problems
1. If a car changes from 10 m/s to 30 m/s in 8 seconds,
what is its acceleration?
v = 30
u = 10
t=8
a = (30 - 10) ÷ 8
= 20 ÷ 8
= 2·5 m/s2
2. If a bicycle moving at 15 m/s takes 10 seconds to stop,
what is its acceleration?
In this example, the final velocity is zero because the bicycle has stopped.
v=0
u = 15
t = 10
a = (0 - 15) ÷ 10
= -15 ÷ 10
= -1·5 m/s2
The acceleration is negative because the bicycle has slowed down.
Acceleration is the rate of change of an objects velocity.
The object is said to have constant acceleration if it gets faster (or slower, or its direction changes) at the
same rate.
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Velocity-Time Graphs
WARNING: In terms of language – non-physicists use the term speed most of the
time! This is OK !!! Although – when the direction counts, i.e. we talk about
objects moving forward and backwards or up and down then we need to use the
term velocity.
The above graph shows that the objects velocity does not change as time goes by.
It is constant velocity. Compare this with the displacement - time graph for constant velocity.
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The above graph shows that the objects velocity is increasing as time goes by.
This is acceleration. The straight line shows that it is constant acceleration.
The slope of the line shows
(i) the acceleration is positive because the line slopes upwards
(ii) how fast the acceleration is.
The above graph shows that the objects velocity is decreasing as time goes by.
This is negative acceleration. The straight line shows that it is constant negative acceleration.
The slope of the line shows
(i) the acceleration is negative because the line slopes downwards
(ii) how fast the negative acceleration is.
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The curve in the above graph shows that the acceleration is not constant. It is changing acceleration.
You may be shown a graph like the one below and be asked to describe the motion of the object.
In region A the object is moving with constant acceleration.
In region B the object is moving with constant velocity.
In region C the object is again moving with constant acceleration
but compared with region A
(i) the acceleration is slower because the slope is less steep
(ii) the acceleration is negative because the slope is downwards.
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The total displacement travelled by the object can be calculated by measuring the area under the graph.
The total displacement travelled by the object can be calculated by measuring the area between the
graph and the baseline. This is called the area under the graph.
The area under the previous graph can be divided into two triangles and one rectangle.
The area of triangle A is half base x height
= 0·5 x 10 x 20 = 100.
The area of triangle C = 0·5 x (70 - 30) x 20 = 400.
The area of rectangle B
= (30 - 10) x 20 = 400.
The distance travelled is the total area = A + B + C
= 100 + 400 + 400= 900 m.
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Forces, Movement and Shape
Forces can be expressed as a push or pull of one body on another.
As you are sitting on your chair, your weight pulls you down. This is the gravitational pull of the Earth on
you. At the same time there is a gravitational pull of your body on the Earth. Exactly, this sounds
surprising. And: as your weight pushes down on the chair you sit on, the chair pushes upwards onto
your body to keep you ‘stationary’. These interactions of forces can be applied to many other situations,
e.g. a car pulling a trailer.
There are various types of forces. Here is a selection of them:

Gravitational force (as mentioned)

Electrostatic force

Magnetic force

Friction, drag, air resistance

Elastic force/force of a spring

Normal reaction force (e.g. of the ground on a car or on your chair)
Friction, drag and air resistance always oppose the motion of an object. This applies to falling apples as
well as to speeding cars.
Addition of Forces, Balanced and Unbalanced Forces, Resultant Force
Driving force
Resultant force
Drag
The tractor has a larger forward force (driving force = 3000N) than drag (1500N). The two forces
(vectors) can be represented by arrows as shown above. The resultant force acting on the tractor is the
difference between the two forces. It can be calculated by subtracting the two vectors. In this case the
resultant force will be F = 3000 – 1500 = 2000N.
Driving force
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Pull from trailer Drag
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In this second example a trailer (only its pull is shown as an arrow) is connected to the tractor. Now the
sum of the pull of the trailer and the drag are equal and opposite to the driving force. The resultant
force is therefore 0N.
In the first case the forward and backward forces are unbalanced, in the second case the forces are
overall balanced.
Force, Mass and Acceleration
When the forces on an object are balanced it will remain stationary if it was stationary before. If it was
moving at constant velocity before, it will continue to do so. This is Newton’s first law of motion. Objects
only accelerate or decelerate when an unbalanced force acts on them. The greater the unbalanced
force, the greater the acceleration.
The acceleration of the object also depends on a second factor. A force of 1000N will accelerate a
bicycle very quickly, but it will very little effect on a coach, let alone a train. Hence mass is the second
factor that influences acceleration. The following formula joins these factors:
Force = mass x acceleration
F
=
m x
a
Units:
F: N (newtons)
m: kg
a: m/s2
The formula shows that 1N = 1kgm/s2. This means that a force of 1N accelerates a mass of 1kg at a rate
of 1 m/s2. In other words, the velocity will increase by 1m/s every second.
Mass & Weight
In Physics the word weight has a different meaning than in daily life. Mass is what you mean when you
talk about ‘losing weight’. From a Physics point of view, you are losing mass, measured in kg (or stones).
Weight is the gravitational pull on an object, it is a force, measured in newtons. You could lose weight by
flying to the moon where the gravitational pull is less.
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Weight is calculated as
Weight = mass x acceleration due to gravity
W
= m x
g
Units:
W: N
m: kg
g: m/s2
On Earth: g = 10 m/s2
If you have a close look at the formula you will find that it is just a special case of F=ma.
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Terminal Velocity
When a skydiver jumps out of a plane only his weight (W = mg) will act on his
body) in the very first instance. As she accelerates and her speed increases, the
air resistance or drag increases as well. The resultant force becomes less. Finally
drag and weight balance each other out. The skydiver falls at a constant
velocity. This is called terminal velocity.
The velocity-time graph looks like this.
Terminal Velocity
The skydiver here reaches a second terminal velocity after the parachute has
been
opened.
Consider
a skydiver:
Due to the initial high velocity the drag is now much bigger than the weight. Once the
skydiver has slowed down, she reaches terminal velocity again, which is much lower this
time as the graph shows. Eventually she lands and her velocity is zero.
4) When he opens his parachute the
air resistance suddenly ________,
causing him to start _____ ____.
5) Because he is slowing down his air
resistance will _______ again until
it balances his _________. The
skydiver has now reached a new,
lower ________ _______.
Terminal velocity occurs on falling objects in liquid as well, e.g. when a stone is thrown into
a lake.
Words – slowing down, decrease,
terminal velocity, weight
21/03/2010
increases,
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Stopping Distances
The distance it takes to bring a car or a bicycle to a halt is called stopping distance. The stopping
distance consists of the thinking distance and the braking distance. The thinking distance is the distance
covered during the reaction time. The vehicle continues travelling at the same speed. Once the brakes
have been applied, the vehicle will slow down and stop. In this time the braking distance is covered.
The following diagram shows how the speed influences the two distances.
The thinking distance increases proportionally to the speed as d = v x t. If you double the speed, the
distance covered in your reaction time doubles as well.
The braking distance increases approximately with the square of the speed (ntk).
The diagram above relates to specific conditions. There are a number of factors that influence both
thinking distance and braking distance.
Factors influencing Thinking Distance Factors influencing Braking Distance
Tiredness
Road conditions (wet, icy, gravel, dry tarmac, etc.)
Alcohol
Quality of tyres
Drugs
Quality of brakes
Distractions (e.g. mobile phone)
Momentum
Momentum is a measure of how difficult it is to stop a moving object. A flying football has a smaller
momentum than a rugby player running at full speed, a train has a larger momentum than a lorry. These
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two examples suggest that there are two quantities that determine the momentum of an object: mass
and velocity.
momentum = mass x velocity
p=mxv
p: momentum (in kgm/s or Ns)
m: mass (in kg)
v: velocity (in m/s)
Momentum is therefore defined as the product of mass and velocity of an object. It is a vector quantity.
Example:
A Golf of mass 1100kg drives at a speed of 13m/s (approx 30mph).
The momentum of the Golf is:
p= mv = 1100 x 13 = 14300 kgm/s
Momentum and Force
If momentum is a measure of how difficult it is to stop a moving object, then force and momentum must
be linked. The force to stop a moving object can be calculated using the following formula:
Force = change in momentum / time taken
F
mv  mu
t
v: final velocity, u: initial velocity
This means that if an object is stopped within a short time, a large force is applied.
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Example:
Find the force it takes to stop a Golf of mass 1100kg at a velocity of 14m/s within 5s.
u = 14m/s
F
v = 0m/s
m = 1100kg
t = 5s
mv  mu 1100  14  1100  0

 3080N
t
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Application:
In road accidents cars are usually stopped within a very short period of time. That means that the forces
acting on the passengers are very high. Even if a person wears a seatbelt, the pull of the seatbelt on the
person could be so high that the person could be injured. Seatbelts are therefore made of slightly
stretchy materials (you cannot notice this when pulling on the material). As they stretch the momentum
of the person is changed over a longer period of time, hence reducing the impact force.
The crumple zones of cars have the same purpose: it takes longer to
stop a car hitting another car when the front crumples than when
there is no crumple zone. Hence the impact forces on the
passengers are smaller. Ntk: A more robust, tank-like car would
probably maintain its shape, but be more harmful to the passengers
inside.
One of the disadvantages of the great Smart
minimal and therefore the potential harm to
However, in the city the speeds are also
car is that the crumple zone is
driver/passengers greater.
lower than on the motorway.
The formula F 
F
mv  mu
can be rewritten as F=ma:
t
mv  mu
v u
v
m
m
 ma
t
t
t
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Momentum, Collisions and Explosion
Momentum is conserved in collisions. That means that the total momentum before a collision equals the
total momentum after the collision.
Total momentum before the collision = total momentum after the collision
The conservation of momentum can be demonstrated with Newton’s
cradle. When one steel ball hits the balls in the middle, one ball on the
right will be moving away with the same momentum as the momentum
of the ball hitting the balls from the left.
In the following example two balls collide. The left one has a mass of
0.5kg, the right one has a mass of 0.2kg. You are supposed to find the velocity of the left one after their
collision.
u1=10m/s
u2=0m/s
collision
v1=5m/s
v2=?
m1u1+m2u2 = m1v1 + m2v2
u2 = 0m/s. Therefore:
0.5 x 10 = 0.5 x 5 + 0.2 x v2
5 = 2.5
+ 0.2 x v2
2.5 = 0.2 x v2
v2 = 12.5 m/s
When one of the objects bounces back after the collision, its
velocity will be negative!
In an elastic collision, the kinetic energy is conserved as well.
This means that the total kinetic energy before and after the
collision will be the same.
In an inelastic collision the two objects stick together after the collision. Kinetic energy is not conserved,
but momentum always is.
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Conservation of momentum is also used to calculate velocities in explosions or rockets.
The change in momentum of the exhaust fumes of the rocket is the same as the change in momentum
of the rocket. As the gas particles in the exhaust fumes are small and light, they have to be pushed out
at very high speeds to have a significant change in momentum of the rocket itself.
Note: if two parts fly away from each other in an explosion, one of the velocities has to be negative.
Newton’s Laws of Motion
Newton developed three laws of motion and you have already understood them all without knowing
what they are. This is so you know what each one of them states explicitely.
1st law of motion: An object at rest will remain at rest unless acted on by an unbalanced force. An object
in motion continues in motion with the same speed and in the same direction unless acted upon by an
unbalanced force.
We said earlier that an object only accelerates (changes its speed) when an unbalanced or resultant
force acts on it. This is the same thing.
2nd law of motion: Acceleration is produced when a force acts on a mass. The greater the mass (of the
object being accelerated) the greater the amount of force needed (to accelerate the object).
This is the formula F = ma put into words. Note: the force here is the resultant force.
3rd law of motion: For every action there is an equal and opposite reaction.
The weight of your body pushing on the chair you are sitting on is the same as the reaction force of the
chair onto your body.
Moments – The Turning Effect of a Force
A force can have a turning effect – it can make an object turn around a fixed pivot
point. The turning effect of a force is called moment.
You pull a spanner at its end rather than close to the nut.
This feels easier. In Physics terms the moment is higher
when you pull the spanner with the same force at the far
end from the nut.
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A pivot or fulcrum is the point around which an object turns, e.g. the nut or in case of a door the hinge.
The moment depends on two factors: the distance of the force from the pivot and the size of the force.
The moment can therefore be calculated as
moment = force x perpendicular distance from pivot
M
= F
x
d
Units:
M: Nm (Newton meters)
F: N
d: m
Examples:
1.
F = 20N
pivot
d = 0.6m
M=Fd
M = 20 x 0.6
M = 12Nm
2. Here the object has been moved and therefore the perpendicular distance between force and pivot
has been shortened from 0.6m to 0.5m.
d = 0.5m
F = 20N
The moment will now be different:
M = 20 x 0.5
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M = 10Nm
Often there are several forces acting on an object. Each force causes a moment. The system will remain
stationary when the moments are balanced. That means that the sum of the moments in clockwise
direction will be equal to the sum of the moments in anti-clockwise direction. The principle of moments
states: The sum of the clockwise moments equals the sum of the anti-clockwise moments for a system
in equilibrium. Equilibrium means balanced forces/moments.
F1=10N
d1=0.2m
d2=0.2m
F2=5N
F3=?
d3=0.3m
The sum principle of moments can be written as following: Σ is the Greek capital letter ‘sigma’, which
stands for ‘sum of’. The arrows show clockwise and anti-clockwise directions.
Σ↺M = Σ↻M
F1 x d1 = F2 x d2 + F3 x d3
10 x 0.2 = 5 x 0.2 + F3 x 0.3
2 = 1 + 0.3 F3
1 = 0.3 F3
F3 = 1/0.3 = 3.33N
The same method can be used to find an unknown distance, if all forces are given.
Centre of Gravity
The centre of gravity is the point through which the whole weight of an object seems to act. For a
symmetrical object this will be in the centre of the object, like on the ruler shown. The weight arrow is
usually shown as an arrow through this point. You might have done this in the past without knowing
that this was the centre of gravity, or centre of mass as it is sometimes called.
If you have an irregularly shaped body, the centre of gravity can even lie outside the body itself:
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d3=0.1m
d1=0.1m
d2=0.3m
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F1=10N
F2=?
W=20N
Σ↺M = Σ↻M
W d3 = F1 d1 + F2 x d2
20 x 0.1 = 10 x 0.1 + F2 x 0.3
2 = 1 + F2 x 0.3
1 = F2 x 0.3
F2 = 3.33N
Stability and centre of gravity
Intuitively we know that it is easier to topple over the vase than the umbrella base. The Physics behind
this is that the moment needed to topple over the vase is much lower than the moment needed to
topple over the base. Generally speaking objects with a low centre of gravity and a broad base are more
difficult to topple over than objects with a high centre of gravity and a small base.
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Forces on a light beam
A light beam is considered to be so light that its own weight is negligible in comparison with the forces
acting on the beam. A light beam could be a beam across a stream with a person walking across it. Or it
could be a very light bridge with a lorry driving across it. No, you don't need to worry whether the very
light bridge will hold the lorry or whether it will collapse ... This is someone else's problem, but you are
right, this idea of the 'light beam' only applies within certain limits.
If a girl stands in the middle of a light beam, half of her weight will be supported by either end.
W
F = -½ W
F = -½ W
If she stands just above the support of the light beam on either end, then this end will support her full
weight, while there will be no force on the other end.
W
F = -W
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However, the girl could also stand somewhere in between. Then the support force on either end of the
beam could be calculated using the principle of moments and the fact that the sum of the upwards
forces will equal the sum of the downwards forces (in this case only one, the weight of the girl) as the
object is in equlibrium. However, all you need to know for the exam is that as the girl walks towards the
left end, the support force on the left increases and the support force on the right decreases. If she
walked towards the right, the opposite would be the case.
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Force-Extension Graphs
When another person stands on your foot, it gets squashed. The weight of the other person compresses
your foot. Materials that go back to their original shapes show elastic behaviour, materials that remain
permanently deformed show plastic behaviour. The word plastic in this context has nothing to do with
the material that shopping bags are made of. When a new phone is designed, it is important that the
casing shows elastic behaviour to a certain extent, e.g. when it is dropped, so that you pick it up and it
looks unchanged. When the impact force on the phone is too high, it would break.
In this context we only look at very simple cases: the extension of a rubber band, of metal helical springs
and of metal wires. A force-extension graph shows how the shape of the rubber changes as the force is
applied.
The force here is not proportional the extension as the line is not straight. (Ntk: This has to do with the
untangling of the polymers as the rubber is stretched.)
Many of us have played with the metal spring in a ballpen. When stretched, the spring goes back to its
original length unless it is stretched too much. The following graph shows the behaviour of a metal
spring under load:
Limit of
proportionality
Breaking point
Hooke’s law applies
Elastic limit (when stretched further, plastic
deformation occurs: the spring will not go back to
its original shape
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At the beginning the force is directly proportional to the extension. The point at the end of the straight
line is called the limit of proportionality. The spring can be stretched a little further and still go back to
its original length when released. The point beyond which the deformation will be plastic is called the
elastic limit. Between the elastic limit and the breaking point of the spring more plastic deformation
takes place.
Hooke’s Law
The first part of the graph is a straight line graph through the origin. The force (or load) is directly
proportional to the extension. Directly proportional means that if you double the force, the extension
will also double.
Hooke’s law describes this behaviour mathematically:
Force = spring constant x extension
F = kx
k: spring constant (in N/m or N/cm)
x: extension (in m or cm)
Note: the extension is the amount by which the spring gets longer, it is not to be confused with the
length of the spring.
Note: the spring constant is the gradient of the graph.
Wires do not seem to stretch as we usually do not notice it with the naked eye. However, they do
stretch just like a spring, just less. The stiffness of a metal wire would therefore be far higher.
How would the graph of a wire look like?
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Astronomy
Moons
Not only does the Earth orbit the Sun, but the Moon also orbits the Earth. Our planet is not the only one
orbited by a moon. Below is a list of various planets and their moons.
Moons are often called ‘natural satellites’ as they orbit a planet. What we call a satellite in daily life
would be an ‘artificial satellite’ in Physics.
Note: for the exam you only need to know that some other planets than the Earth have moons.
Planet
Moons
Names of Moons
Mercury
0
-
Venus
0
-
Earth
1
Luna
Mars
2
Phobos, Deimos
Jupiter
63
Io, Europa, Ganymede, Callisto (Galilean moons);
Amalthea, Himalia, Elara, Pasiphae, Sinope, Lysithea, Carme, Ananke, Leda;
Metis, Adrastea (shepherd moons);
Thebe, Callirrhoe, Themisto, Kalyke, Iocaste, Erinome, Harpalyke, Isonoe, Praxidike,
Megaclite, Taygete, Chaldene, Autonoe, Thyone, Hermippe, Eurydome, Sponde, Pasithee,
Euanthe, Kale, Orthosie, Euporie, Aitne
(+ 25 other moons)
Saturn
61
Titan, Rhea, Iapetus, Dione, Tethys, Enceladus, Mimas, Hyperion;
Prometheus, Pandora (shepherd moons);
Phoebe, Janus, Epimetheus, Helene, Telesto, Calypso, Atlas, Pan, Ymir, Paaliaq, Siarnaq,
Tarvos, Kiviuq, Ijiraq, Thrymr, Skathi, Mundilfari, Erriapo, Albiorox, Suttung
(+ 30 other moons)
Uranus
27
Cordelia, Ophelia, (shepherd moons);
Bianca, Cressida, Desdemona, Juliet, Portia, Rosalind, Belinda, Puck, Miranda, Ariel, Umbriel,
Titania, Oberon, Caliban, Sycorax, Prospero, Setebos, Stephano, Trinculo
(+ 6 unnamed moons)
Neptune
13
Triton, Nereid, Naiad, Thalassa, Despina, Larissa, Proteus, Galatea (shepherd moon)
(+ 5 unnamed moons)
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© Cooke & Nelkin Physics Notes
Triple IGCSE Physics 2011
Vers. 1.0
Gravitational Field Strength
The gravitational field strength on Earth is about 10m/s2 or 10N/kg. As shown above the weight can be
calculated from the mass using the gravitational field strength. The mass will be the same anywhere in
the universe, but the weight changes. On the moon g is only about 1/6 of its value on Earth (about
1.6N/kg). That means that you would weigh only 1/6. You could jump six times
higher than on Earth and you would be able to lift up masses which are six
times as high. Lifting up small rocks would be no problem.
On the bigger, heavier planets the gravitational field strength is higher as they
have a greater mass. On Jupiter it is about 23N/kg, while it is less than 4N/kg on Mars.
Gravity
The Sun and all the planets exist in empty space. The ‘magic’ force that keeps the planets in their orbits
around the Sun is called gravity.
Gravity is the attractive force between masses. It only has a noticeable effect when at least one of the
two masses is huge. Sitting next to your neighbour you do not feel any gravitational attraction. That is
because you do not weigh enough. However, the Earth with its big mass pulls you towards its centre and
keeps you on its surface.
The gravitational force not only keeps planets in their orbit around the sun, but also causes the moon
and artificial satellites to orbit the Earth. The diagram below shows the elliptical paths of the planets
around the Sun. It is an old diagram still containing Pluto as a planet, which obviously no longer is the
case.
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© Cooke & Nelkin Physics Notes
Triple IGCSE Physics 2011
Vers. 1.0
Comets
The paths of comets are also determined by the gravitational pull of the Sun.
The diagram below shows the orbit of the comet Ikeya-Zhang. While the
planets’ orbits are close to circular paths, those of the comets are far more
elliptical.
Comets are about 1-30km in diameter and are made up of dust and ice. As
they get closer to the sun, some of the frozen gases evaporate and are blown away from the Sun (by so
called solar wind). Hence the tail of a comet always points away from the Sun.
Probably the most famous comet is Halley’s comet. It comes close to the Sun every 76 years and was last
visible from Earth in 1986.
Orbital Speed, Orbital Radius and Time Period
Speed = distance/time
The distance covered in one orbit is the circumference of a circle (we assume here that the orbits are
circular): distance = 2πr
The time taken for one orbit is called the ‘time period’ (symbol: T).
Therefore: v 
2 xxorbital  radius
time  period
v
Example: Find the orbital speed of the Earth.
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2r
T
© Cooke & Nelkin Physics Notes
Triple IGCSE Physics 2011
Vers. 1.0
Since the orbit of the Earth around the Sun follows an ellipse, the distance between Sun and Earth
varies. Therefore we take an average here, which is 149,000,000km.
The time period is obviously 1year. To get the speed in km/s (!) we need to convert 1 year into seconds.
T = 1 year = 365days x 24h/day x 60min/h x 60s/min = 31,536,000s
Therefore the speed will be
v
2x149 ,000 ,000
 29 .69 km / s  30 km / s
31,536 ,000
Think: Would the velocity of the Earth be a constant 30km/s as well?
Galaxies
A galaxy is a huge collection of billions of stars. The galaxy that we belong
to is called the Milky Way. It is a spiral type of galaxy similar to that in the
image. As it is so big and we are 2/3 out from the centre, it is absolutely
impossible to obtain any pictures like the one on the right side of our own
galaxy. However, when you are out in the countryside, you can see what
looks like clouds on a clear night sky. There are so many stars and many of
them are so far away, that we just see a lighter stretch across the entire
sky.
The universe again is believed to consist of billions of galaxies. If you are about to get a headache now,
you know that you are getting a grasp of space and its vastness.
This is just scratching the surface of an incredibly topic.
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