Physics | Mechanics, Quantum mechanics » Physics Equations

Source: http://www.doksinet Physics Equations 1 Mechanics 1.1 Dimensional motion 1.3 Projectile motion vy = vyo − gt x = x o + v xo t ~v = ~vo + ~at 1 x = xo + (~v + ~vo )t 2 1 x = xo + ~vo t + ~at2 2 1 2 x = xo + ~v t − ~at 2 ~v 2 = ~vo2 + 2~a(x − xo ) 1 y = yo + vyo t − gt2 2  2 g x y = x tan θ − 2 vo cos θ 2 2 v sin θ ymax = o 2g 2 v sin 2θ xmax = o g 2vo sin θ tmax = g ~rAB = ~rA − ~rB x : Distance, m xo : Initial distance, starting point, m ~v : Velocity, ms−1 ~vo : Initial velocity, ms−1 t : Time, s ~a : Acceleration, ms−2 ~ relative to B ~ ~rAB : Position of A ~ realtive to origin ~rV : Position of V y : Graph of the trajectory t : Time ymax : Maximum y-coord reached by projectile xmax : Maximum x-coord reached by projectile tmax : Time for which projectile airborne 1.4 1.2 Conversions Circular motion v2 4π 2 r = r T2 1 2πr T = = v f ~ac = km · h−1 − m · s−1 Multiply by 5 /18 m · s−1 − km · h−1 Multiply by 18 /5 ~ac :

Cetripetal acceleration T : Period of uniform circular motion f : Frequency, number of revolutions per unit time r : Radius of circle 1 Source: http://www.doksinet 2 Forces 3.1 P~ = m~v F~ = m~a ~y ~x + A ~yB ~•B ~ = cos θ|A||B| = A ~ xB A W = F~ • ∆~r Z x2 f (x)dx W = F~g = m~g F~sp = −kx x1 Z ~r2 ∆P~ = F~ ∆t = m∆~v = J W = F~ • ∆~r (line integral) ~ r1 F~ : Force, N = kg · ms−1 F~g : Gravitational force, kg · m2 s−2 m : Mass, kg ~g : Gravity, −9.81 · kg · ms−2 F~sp : Spring force, N k : Spring constant, N m−1 = kg · m−2 s−2 P~ : Momentum, kg · ms−1 J : Impulse 2.1 Work and Power ∆Ek = Wnet ∆W P = ∆t ~ P = F • ~v Z b ∆EGPab = − F~ • ∆~r a ~•B ~ : Dot product of vectors A ~ and B ~ A ~ |A| : Magnitude, length of vector A ~ ~ Ax : x-parameter of vector A W : Work, J = kg · m2 s−1 P : Power, W = kg · m2 s−2 Friction fs ⩽ µs F~N fk = µk F~N fi : Force of static (i = s) or kinetic (i = k) friction

µi : Coefficient of static (i = s) or kinetic (i = k) friction F~N : Normal force 3 3.2 Energy Torque τ = rF~ sin θ ~τ = ~r × F~ 1 Ek = mv 2 2 EGP = mg∆h 1 EEP = kx2 2 τ = Iα τ : Torque, N m I : Rotational inertia α : Angular acceleration Ek : Kinetic energy EGP : Gravitational potential energy EEP : Elastic potential energy 2 Source: http://www.doksinet 3.3 5 Gravity GM m r2 r GM vorb = r 2 r3 4π T2 = GM Rotational Motion v = ωr F = at = αr (circular orbit) ar = ω 2 r 1 Ek = Iω 2 2 Z X 2 I= mi ri = r2 dm (circular orbit)  1 1 − ∆EGP = GM m r1 r2 r 2GM vesc = r GM gf = − 2 r  ~ = Iω = ~r × p~ L ω r ar at I ~ L G : Universal gravitational constant M : Larger mass (being orbited) m : Smaller mass (in orbit) r : Distance form M to m vorb : Orbital speed vesc : Escape velocity gf : Gravitational field 4 : Angular velocity : Radius of object : Radial acceleration : Tangential acceleration : Rotational inertia : Angular momentum Linear x dx v=

dt Systems of Particles a= P mi~ri M m1 x1 + m2 x2 + . mi xi xcm = m1 + m2 + . mi Eksys = Ekcm + Ekint Angular θ dθ ω= dt dv d2 x = 2 dt dt v = vo + at x = xo + vo t + 12 at2 v 2 = v02 + 2ax ~rcm = 6 ~rcm : Vector position of center of mass xcm : Coordinate position of center of mass mi : ith particle composing larger mass M Unit Distance Impulse dω d2 θ = 2 dt dt ω = ωo + αt θ = θo + ωo t + 12 αt2 ω 2 = ωo2 + 2αθ Miscellaneous Area under Velocity v Time Force v Time J = ∆p = F ∆t = m∆v 3 α=