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Trigonometry and Algebra b Sin 8 Sin A Sinc For a right angle triangle, c = a + b2 For all triangles c? = a + b2 - 2 a b Cos C Cose + Sin e = 1 Differentiation d(ax"=0) = nax-1 Integration Sax"dx = **1 ***1 +C dx ac If a x2 + bx+c=0 then -bt X = Za Motion Force = mass x acceleration Potential Energy = mgh Kinetic Energy = mv Work = Energy Power is rate of work Momentum = Mass x Velocity Impulse = Force x Time Acceleration due to gravity (9) = -9.8 ms? w = 2 T f = (2T)/T Moment of Inertia for a point mass, I =mr Moment of Inertia for disc, I amr? Moment of Inertia for a sphere, I amr Moment of Inertia for a rod pinned at one end I am Moment of Inertia for a rod pinned in the middle I am For a set of masses rotating on the same shaft, I = 1,+ 12+13+14 Acceleration due to gravity (g) = -9.8 ms?
Linear Angular 0 S V w a a dw Q V = u + at w = wo + at V = u' + 2as w = wo" + 2a0 s = ut + zat? 0 = Wot + Wat" S = 1 (u + v)t = /2 (Wow, t dv das d2e dt dt2 dt dt2 Mass m Moment of Inertia I (kg m) F = ma (N) Torque T (Nm) = Fr= la E (Joules) = m v? E (Joules) = 1 w Momentum p = mv (kgms L= I w (kg m?s') ) Power P (Watts) = Fv (N P (Watts) = T W (Nms') ms) Impulse = A (mv) = F At Δ( Ιω) = ΤΔt SHM Period is T = 2n JĘ for as a pendulum, or T = 21 vete for a mass spring system. k is the stiffness of a spring, or the force required to give unit extension.
Electricity V=IR Power = VI R = R1 + R2 + R3 1 + 1+1 R: R2 R3 R Capacitors Area > Permittivity C= Gap Size AQ = 1 At Q=VC C Charge- Volts Energy = Work = QV Capacitor charging V = V.(1 - IT #ek Time Constant C= RC Vo R e RC Waves v = fx The phase difference o = 27 ) y = A sin wt or y = A sin 20 ft y = A sin 217(f. -5)