 Physics

Key Equations

PhysicsKey Equations

5.2Vector Addition and Subtraction: Analytical Methods

 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

5.3Projectile Motion

 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 $R= v 0 2 sin2 θ 0 g R= v 0 2 sin2 θ 0 g$

5.4Inclined Planes

 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 $w ⊥ =wcos(θ)=mgcos(θ) w ⊥ =wcos(θ)=mgcos(θ)$ parallel component of weight on an inclined plane $w || =wsin(θ)=mgsin(θ) w || =wsin(θ)=mgsin(θ)$

5.5Simple Harmonic Motion

 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 $T=2π L g T=2π L g$
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