PHYSICS NOTES
Chapter 1: Kinematics: Describing Motion
Define and use displacement, speed and velocity
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Displacement: the distance travelled in a particular direction; it is a vector quantity.
Speed: the rate of change of the distance moved by an object; it is a scalar quantity.
Velocity: the rate of change of an object’s displacement.
Draw and interpret displacement-time
Understand the differences between scalar and vector quantities and give examples of each
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Displacement is an example of a vector quantity. A vector quantity has both magnitude (size)
and direction. Distance, on the other hand, is a scalar quantity. Scalar quantities have magnitude
only.
Use vector addition to add and subtract vectors that are in the same plane
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Now we can plot the displacement–time graph (Figure 1.10). We want to work out the velocity
of the car over the first 3.0 seconds. We can do this by working out the gradient of the graph,
because: velocity = gradient of displacement−time graph.
We draw a right-angled triangle as shown. To find the car’s velocity, we divide the change in
displacement by the change in time. These are given by the two sides of the triangle labelled Δs
and Δt.
Chapter 17: Gravitational Fields
Describe a gravitational field as a field of force and define gravitational field strength, g.
The gravitational field is the gravitational force per unit mass that would be exerted on a
small mass at that point. It is a vector field, and points in the direction of the force that the
mass would feel.
The strength of the Earth's gravitational field at a particular point. It is defined as the
gravitational force in newtons that acts on a mass of one kilogram. The value of g on the Earth's
surface is taken to be 9.806 N kg-1.
The symbol g is also used to represent the acceleration of a freely falling object in the Earth's
gravitational field. Near the Earth's surface and in the absence of friction due to the air, all
objects fall with an acceleration of 9.8 ms-2.
Represent a gravitational field using lines
Understand the meaning of centre of mass and the use of concept in problems involving
uniform spheres
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The field lines show two things:
 The arrows on the field lines show us the direction of the gravitational force on a mass
placed in the field.
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 The spacing of the field lines indicates the strength of the gravitational field–the further
apart they are, the weaker the field.
The drawing of the Earth’s gravitational field shows that all objects are attracted towards the
centre of the Earth. This is true even if they are below the surface of the Earth. The gravitational
force gets weaker as you get further away from the Earth’s surface – this is shown by the greater
separation between the field lines. The Earth is almost a uniform spherical mass, although it
does bulge a bit at the equator. The gravitational field of the Earth is as if its entire mass was
concentrated at its centre; this is known as its centre of mass. As far as any object beyond the
Earth’s surface is concerned, the Earth behaves as a point mass. Figure 17.4 shows the Earth’s
gravitational field closer to its surface. The gravitational field in and around a building on the
Earth’s surface shows that the gravitational force is directed downwards everywhere and
(because the field lines are very nearly parallel and evenly spaced) the strength of the
gravitational field is virtually the same at all points in and around the building. This means that
your weight is virtually the same everywhere in this gravitational field. Your weight does not
become much less when you go upstairs.
We describe the Earth’s gravitational field as radial, since the field lines diverge (spread out)
radially from the centre of the Earth. However, on the scale of a building, the gravitational field
is uniform, since the field lines are equally spaced. Jupiter is a more massive planet than the
Earth and so we would represent its gravitational field by showing more closely spaced field
lines.
Recall and use Newton’s law of gravitation
Newton considered two point masses M and m separated by a distance r. Each point mass attracts the
other with a force F. (According to Newton’s third law of motion, the point masses interact with each
other and therefore exert equal but opposite forces on each other.) Newton’s law of gravitation states
that any two point masses attract each other with a force that is directly proportional to the product of
their masses and inversely proportional to the square of their separation. Note that the law refers to
‘point masses’ – you can alternatively use the term ‘particles’. Things are more complicated if we think
about solid bodies that occupy a volume of space. Each particle of one body attracts every particle of
the other body and we would have to add all these forces together to work out the force each body has
on the other. Newton was able to show that two uniform spheres attract one another with a force that
is the same as if their masses were concentrated at their centres (provided their centre-to-centre
distance is greater than the sum of their radii). According to Newton’s law of gravitation, we have:
(The force is attractive, so F is in the opposite direction to r.) The gravitational constant G is sometimes
referred to as the universal gravitational constant because it is believed to have the same value, 6.67 ×
10−11 N m2 kg−2, throughout the Universe. This is important for our understanding of the history and
likely long-term future of the Universe. The equation can also be applied to spherical objects (such as
the Earth and the Moon) provided we remember to measure the separation r between the centres of
the objects. You may also come across the equation in the form:
Your weight (the gravitational force on you) depends on your mass and on the mass of the planet you
happen to be standing on. Second, the further away you are from the planet, the weaker its pull. Twice
as far away gives onequarter of the force. This can be seen from the diagram of the field lines in Figure
17.6. If the distance is doubled, the lines are spread out over four times the surface area, so their
concentration is reduced to one-quarter. This is called an inverse square law. Inverse square laws are
common in physics, light or γrays spreading out uniformly from a point source also follow an inverse
square law
We measure distances from the centre of mass of one body to the centre of mass of the other (Figure
17.7). We treat each body as if its mass were concentrated at one point. The two bodies attract each
other with equal and opposite forces, as required by Newton’s third law of motion. The Earth pulls on
you with a force (your weight) directed towards the centre of the Earth; you attract the Earth with an
equal force, directed away from its centre and towards you. Your pull on an object as massive as the
Earth has little effect on it. The Sun’s pull on the Earth, however, has a very significant effect.