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% Document Info
\author{acwood}
\pdfinfo{
  /Title (mechanics-level-2.pdf)
  /Creator (Cheatography)
  /Author (acwood)
  /Subject (Mechanics - Level 2 Cheat Sheet)
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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Mechanics - Level 2 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{acwood} via \textcolor{DarkBackground}{\uline{cheatography.com/42341/cs/12760/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}acwood \\
  \uline{cheatography.com/acwood} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 8th September, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{tabularx}{17.67cm}{X}
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\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Forces, Torque and Equilibrium}}  \tn
% Row 0
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Newtons Laws }}\{\{nl\}\}	{\emph{First Law}} - How things Move \{\{nl\}\}- An object at rest stays at rest unless acted upon by an external force\{\{nl\}\}	- (External Force) Needs a force to get things to move \{\{nl\}\}	-An object in motion stays moving at a constant speed unless acted upon by an external force \{\{nl\}\}	\{\{nl\}\}	{\emph{Second Law}} - How we calaculate the size of a force \{\{nl\}\}	Force = mass x Acceleration\{\{nl\}\}	F=ma\{\{nl\}\}	Any accelerating object and the force that is pushing or pulling it\{\{nl\}\}	\{\{nl\}\}	{\emph{Third Law}} - Forces come in Pairs\{\{nl\}\}	Every action produces an equal and opposite reaction} \tn 
% Row Count 12 (+ 12)
% Row 1
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Force Vectors}}\{\{nl\}\} Use trigonometry to separate the force vector into vertical and horizontal components. \{\{nl\}\}} \tn 
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% Row 2
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Torque}}\{\{nl\}\}	Name of a turning effect that causes rotation\{\{nl\}\}	-Pivot point from centre of mass which it can rotate around. \{\{nl\}\}	Torque is produced if the force that is applied is not directed at the pivot point.\{\{nl\}\}	- Distance Between the pivot point and the point where the force is apple X by the perpendicular component of the force. Unit Nm. \{\{nl\}\}	t=Fd\{\{nl\}\}	The longer or further distance less net force\{\{nl\}\}	Torques Balanced = Stationary or rotate at a constant speed} \tn 
% Row Count 25 (+ 10)
% Row 3
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Equilibrium}}\{\{nl\}\}	Consequence of Newtons First La\{\{nl\}\}	- An object is at equilibrium when it is either stationary or moving at a constant speed \{\{nl\}\}	No net external force (all force down are balanced and all forces up are balanced)\{\{nl\}\}	No net torque(clockwise torque = anticlockwise torque)\{\{nl\}\}} \tn 
% Row Count 32 (+ 7)
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\begin{tabularx}{17.67cm}{X}
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\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Linear Motion}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{17.67cm}}{{\bf{Displacement and Velocity}} \{\{nl\}\}{\emph{Displacement}}\{\{nl\}\} Is measured in metre and takes into the account of the direction. \{\{nl\}\}{\emph{Vectors}}\{\{nl\}\} represented by an arrow - the length of the arrow gives us the vectors magnitude \{\{nl\}\}\{\{nl\}\}{\emph{Velocity}}\{\{nl\}\} desplacement of an object over the time it takes to reach that displacement ms\textasciicircum{}-1\textasciicircum{}. includes direction different direction different velocity \{\{nl\}\} v=d/t} \tn 
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% Row 1
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Acceleration and Kinematic Equations}}\{\{nl\}\}{\emph{Acceleration}}\{\{nl\}\}Rate of and objects velocity - how much the velocity changes divided by time taken, measured in ms\textasciicircum{}-2\textasciicircum{}.\{\{nl\}\}a=v/t\{\{nl\}\}\{\{nl\}\}{\emph{Kinematic Equations}} \{\{nl\}\}	Vf = Vi +at\{\{nl\}\}d=(Vi +Vf)/2 x t\{\{nl\}\}Vf\textasciicircum{}2\textasciicircum{}=Vi\textasciicircum{}2\textasciicircum{} +2ad\{\{nl\}\}d-Vit +1/2 at\textasciicircum{}2\textasciicircum{}} \tn 
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Vectors}}\{\{nl\}\}	{\emph{Vector Operations}}\{\{nl\}\}	Vector has a magnitude and size. When you divid or multiply vector by scalar the magnitude changes but direction does not unless scalar is negative. The magnitude is always positive. Adding vectors add tip to tail then find resultant. resultant goes other way} \tn 
% Row Count 22 (+ 7)
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\begin{tabularx}{17.67cm}{x{5.7358 cm} x{5.5671 cm} x{5.5671 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{17.67cm}}{\bf\textcolor{white}{Momentum and Impulse}}  \tn
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{\bf{Momentum}}\{\{nl\}\}	Mass of an object multiplied by its velocity\{\{nl\}\}	p=mv\{\{nl\}\}	Big objects moving fast have a large momentum used to solve collision problems \{\{nl\}\}	Kgms\textasciicircum{}-1\textasciicircum{} & {\bf{Impulse}}\{\{nl\}\}	Change in Momentum\{\{nl\}\}	- Momentum changes when a force is applied to the object over a certain amount of time \{\{nl\}\}	P=Ft\{\{nl\}\}	To maximise an objects change in momentum you can apply a greater force or apply it over a longer time \{\{nl\}\}	Kgms\textasciicircum{}-1\textasciicircum{} or Ns & {\bf{Conservation of Momentum}}\{\{nl\}\}When a external force acts on an object it changes momentum.\{\{nl\}\}When we consider multiple objects with internal force between them - teh total momentum stays the same\{\{nl\}\}- tells us that the total momentum of a system is always the same\{\{nl\}\}Allows us to solve problems with two objects that collide with each other \{\{nl\}\} net force= 0\{\{nl\}\} P=Pt\{\{nl\}\}P=momentum of first + momentum of second\{\{nl\}\}Pf = momentum of both first and second \tn 
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\begin{tabularx}{17.67cm}{X}
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\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Projectiles and Circular Motion}}  \tn
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Gravitation}}\{\{nl\}\}	Describes what happens to an object when its falling\{\{nl\}\}	When an object is falling the only force acting on it is gravity when we ignore other forces like air resistance\{\{nl\}\}	Constant vertical acceleration 9.8ms\textasciicircum{}-2\textasciicircum{}\{\{nl\}\}	- the gravity can be used in kinematic equations} \tn 
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% Row 1
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Projectiles}}\{\{nl\}\}	Is an object moving through the air under the influence of gravity . doesn't have its own power source\{\{nl\}\}	Ignore air resistance. Gravity only force acting on the projectile while in the air.. The vertical component changes in the velocity vector and accelerates downwards at 9.8ms \textasciicircum{}-2\textasciicircum{}through the whole fight. \{\{nl\}\}	The Horizontal component does not change. \{\{nl\}\}	The path is perfectly symmetrical - the speed going up = the speed coming down \{\{nl\}\}	Find the x an y components by using trig.} \tn 
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Circular Motion}}\{\{nl\}\}	Concerns any object that moves around in a circle.\{\{nl\}\}	Even if the speed is constant it keeps changing direction meaning the velocity is always changing. \{\{nl\}\}	a change in velocity over time produces acceleration. acceleration directed at the centre of the circle - call it centripetal acceleration\{\{nl\}\}	Acceleration X mass = centripetal force. this force is directed at the centre of the circle. responsible for keeping object on the circle. \{\{nl\}\}	Velocity is at a tangent to the circle at right angles to the force \{\{nl\}\}	Ac=v\textasciicircum{}2\textasciicircum{}/r\{\{nl\}\}	Fc=mv\textasciicircum{}2\textasciicircum{}/r\{\{nl\}\}	v=speed, m= mass, r= radius} \tn 
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\begin{tabularx}{17.67cm}{X}
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\mymulticolumn{1}{x{17.67cm}}{\bf\textcolor{white}{Energy, Work and Power}}  \tn
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Mechanical Energy and Springs}}\{\{nl\}\}	Spring is a device that stores all elastic potential energy- stretched or compressed.\{\{nl\}\}	amount of energy stored is:\{\{nl\}\}	Ep = 1/2kx\textasciicircum{}2\textasciicircum{}\{\{nl\}\}	K= spring constant(stiffness of the spring) the higher K is the more force need to stretch or compress \{\{nl\}\}	x = change in length ( the distance it is stretched or compressed). This does not include the normal length of the spring. \{\{nl\}\}	When the spring is stretched or compressed there is no elastic potential energy.\{\{nl\}\}	\{\{nl\}\}	{\emph{Hooke's Law}}\{\{nl\}\}	F=-kx\{\{nl\}\}	shows the amount of force required to stretch or compressed a string by a certain amount\{\{nl\}\}	(Negative sign ignored)} \tn 
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% Row 1
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\mymulticolumn{1}{x{17.67cm}}{{\bf{Work and Power}}\{\{nl\}\}	{\emph{Work}}\{\{nl\}\}	Force required to move an object across a certain distance\{\{nl\}\}	W=Fd\{\{nl\}\}	measured in Joules (J)\{\{nl\}\}	Energy is the input the output is work \{\{nl\}\}\{\{nl\}\}	{\emph{Power}}	\{\{nl\}\}	P=W/t \{\{nl\}\}	measured in watts (W)\{\{nl\}\}	\{\{nl\}\}	{\emph{Conservation of Energy}}\{\{nl\}\}	Energy never goes away, it cannot be created or destroyed only transferred from one form to another} \tn 
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