Physics GRE Cheatsheet
Contents
Physics GRE Cheatsheet#
Classical Mechanics#
Kinematics#
2nd Order Displacement :
 
$\(\Delta x = \frac{1}{2} a_0^2 + v_0^2t\)$Velocity Upon Acceleration Given Displacement :
 
\[v_f^2 - v_i^2 = 2a \Delta x\]
Circular Motion#
Centripetal Force (Radial Force) :
 
\[F_r = \frac{mv^2}{r} = m\omega r\]
Special Relativity#
Time Dilation :
 
$$
\Delta x = \frac{\Delta x' }{\sqrt{1-(v/c)^2}}
$$
Length Contraction :
 
$$
\Delta x = \Delta x' \sqrt{1-(v/c)^2}
$$
Energy-Mass Equivalence :
 
\[\begin{split}
\begin{gather}
m = \frac{m_0}{\sqrt{1 - (v/c)^2}}\\
\Big\Downarrow\\
E = mc^2 \tag{Second Order $m$ Expansion}
\end{gather}
\end{split}\]
Identities#
\[
u^2 = \frac{u'c^2}{c^2-v^2} \iff u = \frac{u'}{\sqrt{1-(v/c)^2}}
\]