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equation sheet

# equation sheet - Constant Acceleration v = v0 at 2 x x0 =...

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Constant Acceleration v = v 0 + at x –x 0 = v 0 t + (1/2)at 2 v 2 = v 0 2 + 2a(x – x 0 ) x – x 0 = (1/2)(v 0 + v)t x – x 0 = vt – (1/2)at 2 Range = (v 0 2 /g) sin(2 Ѳ o ) Cross Product C = absin , = angle between two Ѳ Ѳ vectors a = (a x 2 + a y 2 ) tan = (a Ѳ y /a x ) Uniform Circular Motion a = v 2 /r (centripetal acceleration) T = 2 r/v (period) π T = 2 / π ω F = m(v 2 /R) Relative Motion v PA = v PB + v BA Tension T – mg = ma T = Mmg/(M+m) a = mg/(M+m) Friction f k = u k F N f s,max = u s F N When pushing at angle, N = mg + Fsin Ѳ When pulling at angle, N = mg - Fsin Ѳ u s = tan Ѳ Drag D = (1/2)CpAv 2 C = drag coefficient, p = air density, A = effective cross-sectional area V t = (2F g /CpA) K = (1/2)mv 2 Work W = Fd cos Ѳ W = F . d W g = mdg cos Ѳ W = ( τ Ѳ f Ѳ i ) W = K f - K i Springs F x = -kx W s = ½ kx i 2 – ½ kx f 2 Power = F . v (instant) P avg = W/ t Δ P = τω P = F · v (instantaneous power) K 2 + U 2 = K 1 + U 1 E mec = K + U Center of mass = x com = (m 1 x 1 + m 2 x 2 ) / (m 1 + m 2 ) Momentum P = mv F net = dP/dt KE = p 2 /2m Impulse = p Δ P f – p i = J Elastic Collisions V 1f = [(m 1 -m 2 )/(m 1 +m 2 )]v 1i + [2m 2 / (m 1 +m 2 )]v 2i

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