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General Equations

# General Equations - PHYSICS FORMULAS 2426 Electron =-1-19 C...

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PHYSICS FORMULAS 2426 Electron = -1.602 19 × 10 -19 C = 9.11 × 10 -31 kg Proton = 1.602 19 × 10 -19 C = 1.67 × 10 -27 kg Neutron = 0 C = 1.67 × 10 -27 kg 6.022 × 10 23 atoms in one atomic mass unit e is the elementary charge: 1.602 19 × 10 -19 C Potential Energy, velocity of electron: PE = eV = ½ mv 2 1V = 1J/C 1N/C = 1V/m 1J = 1 N·m = 1 C·V 1 amp = 6.21 × 10 18 electrons/second = 1 Coulomb/second 1 hp = 0.756 kW 1 N = 1 T·A·m 1 Pa = 1 N/m 2 Power = Joules/second = I 2 R = IV [watts W ] Quadratic Equation: x b b ac a = - ± - 2 4 2 Kinetic Energy [J] KE mv = 1 2 2 [Natural Log: when e b = x , ln x = b ] m: 10 -3 μ : 10 -6 n: 10 -9 p: 10 -12 f: 10 -15 a: 10 -18 Addition of Multiple Vectors: r r r r R A B C = + + Resultant = Sum of the vectors r r r r R A B C x x x x = + + x -component A A x = cos θ r r r r R A B C y y y y = + + y -component A A y = sin θ R R R x y = + 2 2 Magnitude (length) of R q R y x R R = - tan 1 or tan q R y x R R = Angle of the resultant Multiplication of Vectors: Cross Product or Vector Product: i j k × = j i k × = - i i × = 0 Positive direction: i j k Dot Product or Scalar Product: i j = 0 i i = 1 a b = ab cos q k i j Derivative of Vectors: Velocity is the derivative of position with respect to time: v k i j k = + + = + + d dt x y z dx dt dy dt dz dt ( ) i j Acceleration is the derivative of velocity with respect to time: a k i j k = + + = + + d dt v v v dv dt dv dt dv dt x y z x y z ( ) i j Rectangular Notation: Z R jX = ± where + j represents inductive reactance and - j represents capacitive reactance. For example, Z j = + 8 6 means that a resistor of 8 is in series with an inductive reactance of 6 . Polar Notation: Z = M q , where M is the magnitude of the reactance and q is the direction with respect to the horizontal (pure resistance) axis. For example, a resistor of 4 in series with a capacitor with a reactance of 3 would be expressed as 5 -36.9° . In the descriptions above, impedance is used as an example. Rectangular and Polar Notation can also be used to express amperage, voltage, and power. To convert from rectangular to polar notation: Given: X - j Y ( careful with the sign before the ”j”) Magnitude: X Y M 2 2 + = Angle: tan θ = - Y X (negative sign carried over from rectangular notation in this example) Note: Due to the way the calculator works, if X is negative, you must add 180° after taking the inverse tangent. If the result is greater than 180°, you may optionally subtract 360° to obtain the value closest to the reference angle. To convert from polar to rectangular (j) notation: Given: M q X Value: M cos θ Y (j) Value: M sin θ In conversions, the j value will have the same sign as the q value for angles having a magnitude < 180°. Use rectangular notation when adding and subtracting. Use polar notation for multiplication and division. Multiply in polar notation by multiplying the magnitudes and adding the angles. Divide in polar notation by dividing the magnitudes and subtracting the denominator angle from the numerator angle.

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