Published on Texas Gateway (https://texasgateway.org)
Key Equations
resultant magnitude R= R x 2 + R y 2 R= R x 2 + R y 2
resultant direction θ= tan −1 ( R y / R x ) θ= tan −1 ( R y / R x )
x-component of a vector A (when an angle is given relative to the horizontal) A x =Acosθ A x =Acosθ
y-component of a vector A (when an angle is given relative to the horizontal) A y =Asinθ A y =Asinθ
addition of vectors A x  +  A y  = A A x  +  A y  = A
angle of displacement θ= tan −1 (y/x) θ= tan −1 (y/x)
velocity v= v x 2 + v y 2 v= v x 2 + v y 2
angle of velocity θ v = tan −1 ( v y / v x ) θ v = tan −1 ( v y / v x )
maximum height h= v 0y 2 2g h= v 0y 2 2g
range R= v 0 2 sin2 θ 0 g R= v 0 2 sin2 θ 0 g
force of static friction f s ≤ μ s N f s ≤ μ s N
force of kinetic friction f k = μ k N f k = μ k N
perpendicular component of weight on an inclined plane w ⊥ =w cos(θ)=mg cos(θ) w ⊥ =w cos(θ)=mg cos(θ)
parallel component of weight on an inclined plane w || =w sin(θ)=mg sin(θ) w || =w sin(θ)=mg sin(θ)
Hooke’s law F=−kx F=−kx
period in simple harmonic motion T=2π m k T=2π m k
frequency in simple harmonic motion f= 1 2π k m f= 1 2π k m
period of a simple pendulum T=2π L g T=2π L g