Mechanics

Force

Force=mass*acceleration (F=ma)
Weight=mass*gravitational field strength (W=mg)

The weight of a body is defined as the force exerted on the body by the gravity of a planet

The moment of a force about a point is calculated by T=Force * distance from line of action of the force to the point (T=Fs)

Normal contact forces These contact forces occur between bodies which are touching. In the absence of friction the direction of this force is always normal to the point of contact.
Friction forces Friction occurs between between bodies in contact. It is always parallel to the surface at the point of contact.
Fluid Upthrust-Archimedes Principle states the upthrust which acts on a body which is wholly or partly immersed in a fluid is equal to the weight of the fluid which is displaced.

Forces can have no effect in a direction perpendicular to their line of action.

Dynamics

Motion-related quantities

Displacement is the distance moved by a body in a specified direction, therefore it can be positive or negative depending on the direction from the starting point.
Speed is the rate of change of distance. It is scalar and so is always positive.
Velocity is defined as the rate of change of displacement. It is a vector and so it can be positive or negative depending on direction of motion.
Acceleration is the rate of change of velocity. It is a vector and so it can be positive or negative depending on whether the velocity is increasing or decreasing and on the direction of motion.

Linear Equations

u = initial velocity (i.e when time t=0)
v = final velocity (i.e when time t=t)
a = constant acceleration
s = change of displacement during the time interval
t = time interval

v=u+at
s=((u+v)/2)*t)
s=ut+1/2at²
v²=u²+2as

If any three of the quantities are known then the other two can be calculated using the above equations.

Projectile Motion:

g here is of course gravity = -9.8m/s²

x=(v₀cosα₀)t
y=(v₀sinα₀)t-1/2gt²
v_x=(v₀cosα₀)
v_y=(v₀sinα₀-gt)

Newtons Laws of Motion

Newtons First Law All bodies will continue to be stationary or to move with uniform velocity unless they are acted upon by a resultant force(i.e another force).

Newtons Second Law The rate of change of momentum of a body is directly proportional to the applied resultant force, and occurs in the direction of the resultant force. From this we get the below equation

Momentum=mass*velocity (p=mv)

Newtons Third Equation If body A exerts a force on body B, then body B exerts an equal force in the opposite direction on body A.

Work and Energy

Work is done when a force moves its point of application in the direction in which the force acts

Work=force*distance (W=Fs) This is elementary in any work equation

If the work is done at an angle a then W=Fscosa

Kinetic Energy is given by E_k = 1/2*mass*(velocity²) W=(1/2mv²)

Potential Energy is given by E_p = mass*gravatational field strength*change in height W=(mgΔh)

Elastic Potential Energy is given by E_L=1/2*spring constant*(extension)² W=(1/2kΔl²)

Power is given by

(i) P = Force*velocity (P=Fv)
(ii)P = Work Done / Time Taken (P=ΔW/Δt)

Efficiency is given by %E = (Energy input/Energy output)*100%

Circular Motion and Rotation

Angular velocity is given by: w = 2πf

w=2π/T has units of (rad s^-1)
Also from T=1/f then substitution yields w=2πf

Linear speed of the body is given by v=radius*angular velocity v=rw

Centripetal acceleration is given by

a=v²/r and acts towards the centre of circular path (see right---->)
a=w²r

Centripetal Force is given by F=mv²/r

For Rotational Motion of Rigid bodies then:

Resultant torque is given by T=Moment of inertia*angular acceleration T=Iα
Rotational Kinetic Energy is given by E_k=1/2Iw²
Angular Momentum is given by L=Iw

Gravatation

Every particle in the universe attracts every other particle with a force which is directly proportional to the products of their masses, and inversely proportional to the square of the distance between them.

From this statement we get the Newtons law of gravatational attraction F=-(Gm₁m₂)/r²

where G=universal gravatatational. constant 6.67*10^-11Nm²kg^-2 and m₁ and m₂ are any two point masses. The minus sign represents attractive fields and is convention.

The velocity of a satellite in a cicular orbit is given by v=√(GM/r)

M is the mass of the planet and r is the radius or orbit

Time taken for one orbit is given by T=2π√(R³/GM)

Relationship between g and G is given by: g=- GM/r²

Gravatational Potential is given by E_p=- GMm/r

where M represents the mass of the planet
m is the mass of a body at a distance r from the centre of the planet