Physics | Mechanics, Quantum mechanics » Physics Equations

Source: http://www.doksinet Physics Equations 1 1.1 Mechanics 1.3 Projectile motion Dimensional 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 : xo : ~v : ~vo : t : ~a : ~rAB : ~rV : 1.2 Distance, m Initial distance, starting point, m Velocity, ms−1 Initial velocity, ms−1 Time, s Acceleration, ms−2 ~ relative to B ~ Position of A ~ realtive to origin Position of V y t ymax xmax tmax : : : : : 1.4 Circular motion Conversions Graph of the trajectory Time Maximum y-coord reached by projectile Maximum x-coord reached by projectile Time for which projectile airborne 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 T f r 1 : : : : Cetripetal acceleration Period of uniform circular motion Frequency, number of revolutions per unit time Radius of circle Source: http://www.doksinet 2 Forces 3.1 P~ = m~v F~ = m~a F~g = m~g ~y ~x + A ~yB ~•B ~ = cos θ|A||B| = A ~ xB A W = F~ • ∆~r Z x2 f (x)dx W = F~sp = −kx ∆P~ = F~ ∆t = m∆~v = J F~ F~g m ~g F~sp k P~ J 2.1 Work and Power x1 ~ r2 Z W = F~ • ∆~r (line integral) ~ r1 : : : : : : : : Force, N = kg · ms−1 Gravitational force, kg · m2 s−2 Mass, kg Gravity, −9.81 · kg · ms−2 Spring force, N Spring constant, N m−1 = kg · m−2 s−2 Momentum, kg · ms−1 Impulse ∆Ek = Wnet ∆W P = ∆t ~ P = F • ~v Z ∆EGPab = − b F~ • ∆~r a ~•B ~ A |A| ~x A W P Friction fs 6 µs F~N fk = µk F~N : : : : : ~ and B ~ Dot product of vectors A ~ Magnitude, length of vector A ~ x-parameter of vector A Work, J = kg · m2 s−1 Power, W = kg · m2 s−2 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  G : M : m : r : vorb : vesc : gf : 4 ~ = Iω = ~r × p~ L ω r ar at I ~ L Universal gravitational constant Larger mass (being orbited) Smaller mass (in orbit) Distance form M to m Orbital speed Escape velocity Gravitational field : : : : : : 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=