Key Equations

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

angle of displacement

θ = \tan^{- 1} (y / x)

velocity

v = \sqrt{v_{x}^{2} + v_{y}^{2}}

angle of velocity

θ_{v} = \tan^{- 1} (v_{y} / v_{x})

maximum height

h = \frac{v_{0 y}^{2}}{2 g}

range

R = \frac{v_{0}^{2} \sin 2 θ_{0}}{g}

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}}