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Unformatted text preview: 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 × = Positive direction: i j k Dot Product or Scalar Product: i j ⋅ = 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 Ω means that a resistor of 8 Ω is in series with an inductive reactance of 6 Ω . 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 Ω in series with a capacitor with a reactance of 3 Ω would be expressed as 5 ∠-36.9° Ω . 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°....
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