Motion
Distance: How far something travels
Displacement: The change in position of an object is known as displacement.
Relative velocity:
 E.g two objects move towards each other at 5m/s. The velocity of the object on the left relative to the object on the right is 10m/s.
Relative velocity
An object's velocity is relative to another object.
 E.g two objects move towards each other at 5m/s. The velocity of the object on the left relative to the object on the right is 10m/s.
Relative Velocity can be found by adding the vectors:
Practise Question
Samantha walks along a horizontal path in the direction shown. The curved part of the path is a semicircle.
The magnitude of her displacement from point P to point Q is approximately
A. 2 m.
B. 4 m.
C. 6 m.
D. 8 m.
Answer: D
Graphing motion
Quantities represented by gradient and area of a graph
The Gradient Velocitytime: Acceleration
The area under Velocitytime: Displacement
The area under displacementtime: Velocity
Equations of uniformly accelerated motion
The equations for uniformly accelerated motion are also known as the kinematic equations. They are listed here:
Displacement with acceleration: S= u·t + at22
Velocity equation: V= u+a·t
Timeless: V2= U2 + 2as
Displacement with velocity: s=(u+v)t 2
You do not need to know these as they are in your formula booklet.
Symbol  Definition 
s = ... m  Displacement 
u = ... ms^{1}  Initial Velocity 
V = ... ms^{1}  Final Velocity 
a = ... ms^{2}  Acceleration 
t = ... s  Time 
During exams use suvat, and make sure to fill out with the known variables, and figure out which equation uses all the known variables.
Practise Question
A ball is thrown up with a speed of 20ms^{1}. How long does it take to fall back down to the same starting point?
A: 2.04s
B: 5.09s
C: 4.08s
D: 6.12s
Answer: C
Forces
Forces are vectors as they have a magnitude and a direction
Types of forces
Force 
Description 
Properties 
Symbol 
Applied Force 
Force caused when an object comes in contact with another object 
Either a pull or a push 
F_{a} 
Weight 
Force due to gravity. 
mass *acceleration due to gravity 
W 
Friction 
Force opposing motion and and 
parallel to the contact surface 
F_{f} 
Normal force 
Reaction force to weight 
Equal To weight on a flat surface and perpendicular to surface. 
R 
Tension 
Pull force caused by a rope being tight 
Always a pull 
T 
Spring 
Force caused by an elastic object, such as spring 
F_{e} 

Drag 
Friction in a medium 
Increases with speed. 
F_{d} 
Buoyancy 
Force caused by differences in density. 
F_{b} 
Free body diagrams
To draw a free body diagram draw a dot, and then draw vector arrows coming out from the dot to represent the forces.
There are three things you must do:
 The tail of the vector must touch the dot
 Arrows must be proportional to the forces. E.g if one force is 5N and the other is 10N, then the 10N arrow must be twice the size of the 5N one.
 Arrows must be labeled with the magnitude of force (in newtons) and the type of force
Newton's First Law
An object will remain at rest if there is no net force acting on it
If ΣF = 0, then v = const
ΣF = 0 is the condition for translational equilibrium
Inertia  matters tendency to not change its state of motion (or a state of rest)
Newton's Second Law
If the net forces are more than zero, the velocity will change.
The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.
Net force = mass times acceleration
ΣF = M*A
Momentum version
ΣF = △p/△t
Newton's Third Law
For every action force, there is an equal and opposite reaction force.
FA = FB
Friction
Friction at the atomic level
At an atomic level, an object's surface is never perfectly smooth and is always made of small “peaks”. When objects come in contact, in reality only these peaks are touching and where this occurs weak bonds form, connecting the objects. When an object is pushed the forces are broken between the atoms. Breaking these bonds requires energy and this is what friction is.
Dynamic vs Static phase
When an object is not moving it is in the static phase and the bonds must be broken, for the object to move. However, after the initial bonds are broken an object can move fast enough that the bonds don’t have time to reform. This is the dynamic phase and since not all bonds have to be broken the friction force is lower.
Coefficient of friction
Friction force depends on two variables the normal force and the coefficient of friction.
The coefficient of friction is simply the ratio between the normal force and the friction force.
μ = friction coefficient (it has no units)
μ =Ff/R
There are a friction coefficient μs when it is static and a different one μd When it is dynamic
Therefore, friction depends on how hard an object is pushing on a surface and how slippery the materials are.
Dynamic vs Static Friction
Friction type 
When? 
Relation with applied force. 
Equation 
Symbol 
Static 
The object is in motion 
Always equal to the applied force 
Ff ≤ μs*R 
Fs 
Dynamic 
Object is still 
A constant force which does not change with applied force. 
Ff = μd*R 
Fd 
Why is the friction force lower on an incline?
If an object is on a slope the weight force acts partly parallel to the surface and partly perpendicular to the surface. Weight force can be split into these two components FII and F⊥
As the normal force is equal to the force being exerted perpendicular to the surface. R = F⊥ . Therefore the normal force is decreased on a slope. The acceleration due to gravity is the parallel component FII and this is why an object will slide due to gravity.
Therefore as friction depends on the normal force and this is lower on slopes, things will have a lower friction force when on an incline
Energy
Law of conservation of energy: Energy cannot be made or destroyed; it can only be turned from one form into another.
There are two types of energy: potential and kinetic.
Potential energy  stored energy
Elastic potential equation = ½ * spring constant(k) * x2
Gravitational potential = Mass*Gravity*Height =m*g*h or Weight*Height = w*h
Kinetic Energy  the Energy of Motion
Kinetic energy equation = ½ *m*v2
Efficiency
In theory, things should transfer 100% of their energy from one form to another but in the real world, some energy is lost to things like heat, sound or light. The efficiency of an energy transformation is the percentage of energy in the output compared to the input.
Work
In Physics, we define work(W) as:
 force (F) times the displacement (s) in the direction of the force
 W=F*s*cosθ
The unit for work is newton meters (Nm) or Jules(j)
Note: Work is the same as energy.
Momentum
Momentum = mass * Velocity
P = m*V
Proving Newton's second law momentum equation
Firstly, mass is substituted for momentum over acceleration in Newton's second law.
Fnet=m·a m =∆p∆vFnet=∆p∆v·a
Then, velocity and acceleration are replaced with their distance & time equivalents. This shows why acceleration mostly cancels out velocity, leaving just time.
Fnet=∆p∆ds1*∆ds2
Fnet=∆p∆t
Conservation momentum
In a closed system, if the net force remains the same before and after so will the momentum.
This can be easily proved as if you set net force to zero in the momentum equation you know either delta momentum or deltatime must be zero for both sides to be equal. However, as the change in time cannot be zero, so the change in momentum must be zero.
0 = △p/△t
0 = 0/△t
Momentum before = Momentum after
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