Physics GRE Cheatsheet

Tips Table

Classical Mechanics

Kinematics

2nd Order Displacement :

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$\(\Delta x = \frac{1}{2} a_0^2 + v_0^2t\)$

Velocity Upon Acceleration Given Displacement :

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\[v_f^2 - v_i^2 = 2a \Delta x\]

Circular Motion

Centripetal Force (Radial Force) :

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\[F_r = \frac{mv^2}{r} = m\omega r\]

Special Relativity

Time Dilation :

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$$
\Delta x = \frac{\Delta x' }{\sqrt{1-(v/c)^2}}
$$

Length Contraction :

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$$
\Delta x = \Delta x' \sqrt{1-(v/c)^2}
$$

Energy-Mass Equivalence :

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\[\begin{split} \begin{gather} m = \frac{m_0}{\sqrt{1 - (v/c)^2}}\\ \Big\Downarrow\\ E = mc^2 \tag{Second Order $m$ Expansion} \end{gather} \end{split}\]

Identities

\[ u^2 = \frac{u'c^2}{c^2-v^2} \iff u = \frac{u'}{\sqrt{1-(v/c)^2}} \]