Average Velocity 0 0 x x v t t − = − Instantaneous Velocity 0 lim t x v t → = Average Acceleration 0 0 v v v a t t t − = = − Instantaneous Acceleration 0 lim t v v t → = Kinematics/Straight Line Equations (Constant Acceleration) 0 0 2 0 2 2 0 1 ( ) 2 12 2 v v at x v v t x v t at v v ax = + = + = + = + Newton’s Second Law of Motion F a m F ma ∑ = ∑ = Newton’s Law of Universal Gravitation 1 2 2 11 2 2 6.67259 10 /m m F G r G N m kg − == ⋅ ⋅ Apparent Weight N F mg ma = + Static Frictional Force MAX s s N f F µ = Kinetic Frictional Force k k N f F µ = Uniform Circular Velocity 2 r v Tπ = Centripetal Acceleration 2 c v a r = Centripetal Force 2 c mv F r = Velocity in Circular Orbits E GM v r = Work (Done by a Constant Force) ( cos ) W F s θ = Kinetic Energy 2 12 KE mv = Work-Energy Theorem 2 2 0 0 1 1 2 2 f f W KE KE mv mv = − = − Work Done by Gravity 0 0 ( cos )( ) ( ) f f W mg h h mg h h θ = − = − Gravitational Potential Energy PE mgh = Work Done by Non-Conservative Forces ( ) 2 2 0 0 1 1 ( ) 2 2 NC f f W mv mgh mv mgh = + − + Average Power _ W P t P F v == Impulse Impulse F t = Linear Momentum p mv = Impulse-Momentum Theorem 0 f F t mv mv = − Center of Mass 1 1 2 2 1 2 cm m x m x x m m + = + Velocity of Center of Mass 1 1 2 2 1 2 cm m v m v v m m + = + Average Angular Velocity 0 0 t t t θ θ θ ω − = = − Average Angular Acceleration 0 0 t t t ω ω ω α − = = − Tangential Velocity T V r ω = Tangential Acceleration T a r α =