Vectors and Scalars
Vector: A quantity with both magnitude and direction
Scalar: A quantity with only magnitude
Examples
Vectors 
Scalars 
velocity 
Mass 
displacement 
Time 
Weight 
Distance 
Acceleration 
Length 
Ways of representing a vector
 A plus or minus next to the magnitude
 F = +5N
 An arrow next to the magnitude
 F = 5N ⟶
 A direction next to the magnitude
 F = 5N right
 An angle next to the magnitude (angles always starting from positive x axis like unit circle)
 F = 5N 0°
Vector addition and subtraction graphically:
S= A+B
To add two vectors, draw the first vector with its tail at the origin and then draw the second vector with its tail at the previous vectors head. FInally draw a line form the origin to the head of the second vector. This line is the new vector, as shown below.
S= AB
To subtract a vector, do the same as with addition but flip the vector which you are subtracting.
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 
Fa 
Weight 
Force due to gravity. 
mass *acceleration due to gravity 
W 
Friction 
Force opposing motion and and 
parallel to the contact surface 
Ff 
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 
Fe 

Drag 
Friction in a medium 
Increases with speed. 
FD 
Buyant 
Force caused by differences in density. 
FB 
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:
 Tail of 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 magnitude of force (in newtons) and the type of force
Motion
Quantities of motion
Displacement(s): Distance from starting point
Velocity(v): displacement / time
Acceleration(A): change in velocity/time
Relative velocity: an object's velocity 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 the right is 10m/s.
Equations of motion
The equations for uniformly accelerated motion are also known as the kinematic equations. They are listed here
S= ut + (½)at2 Displacement with acceleration
V= u+at Velocity equation
V2= U2 + 2as Timeless
s=(u+v)t/2 Displacement with velocity
S = displacement
U = initial velocity
V = final velocity
A = acceleration = V/t
T= time
Use suvat, make table fill it out with the known variables, and figure out which equation uses all the known variables.
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 intermolecular bonds form, connecting the objects. When an object is pushed the intermolecular 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 intermolecular 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 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 is 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 
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 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
Newton's laws
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 it’s state of rest)
Newton's second Law
If the net forces is 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 accelleration
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
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  energy of motion
Kinetic energy equation = ½ *m*v2
Efficiency
In theory thing should transfer 100% of their energy form one form to another but in the real world some energy is lost to thing slike 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 metres (Nm) or Jules(j)
Note: Work is the same as energy.
Momentum
Momentum = mass * Velocity
P = m*V
Proving the newton's second law momentum equation
Firstly, mass is subsituted for momentum over acceleratiion in newtons second law.
${F}_{net}=m\xb7a\phantom{\rule{0ex}{0ex}}m=\frac{\u2206p}{\u2206v}\phantom{\rule{0ex}{0ex}}{F}_{net}=\frac{\u2206p}{\u2206v}\xb7a$
Then, velcocity and acceleration are replaced with their distance & time equivalents. This shows why acceleration mostly cancels out velocity, leaving just time.
${F}_{net}=\frac{\u2206p}{\u2206d{s}^{1}}*\u2206d{s}^{2}$
${F}_{net}=\frac{\u2206p}{\u2206t}$
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 delta time must be zero for both sides to be equal. However as change in time cannot be zero, so change in momentum must be zero.
0 = △p/△t
0 = 0/△t
Momentum before = Momentum after
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 joeClinton  2387 words.
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