Key Equations - Physics

resultant magnitude	$R = \sqrt{R_{x}^{2} + R_{y}^{2}}$
resultant direction	$θ = {tan}^{- 1} (R_{y} / R_{x})$
x-component of a vector A (when an angle is given relative to the horizontal)	$A_{x} = A cos θ$
y-component of a vector A (when an angle is given relative to the horizontal)	$A_{y} = A sin θ$
addition of vectors	$A_{x} + A_{y} = A$

force of static friction	$f_{s} \leq μ_{s} N$
force of kinetic friction	$f_{k} = μ_{k} N$
perpendicular component of weight on an inclined plane	$w_{⊥} = w cos (θ) = m g cos (θ)$
parallel component of weight on an inclined plane	$w_{\| \|} = w sin (θ) = m g sin (θ)$

Hooke’s law	$F = - k x$
period in simple harmonic motion	$T = 2 π \sqrt{\frac{m}{k}}$
frequency in simple harmonic motion	$f = \frac{1}{2 π} \sqrt{\frac{k}{m}}$
period of a simple pendulum	$T = 2 π \sqrt{\frac{L}{g}}$