Equations Flashcards
Velocity
Position/Time = L/T
unit: m/s
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object’s speed and direction of motion (e.g. 60 km/h to the north)
Acceleration
Velocity/time = (L/T) / T = L / (T^2)
Unit: m/(s^2)
Force
F = mass * acceleration = (M*L)/(T^2) =
(Kg * M) / (S^2)
Unit: Newton (N)
Pressure
Total force / surface area =
(M * L * T^2-) / (L^2) = M / L*(T^2)
Unit: N/(m^2) or pascal (pa)
Static friction forces
Fs = μs * N
N: Normal forces
Kinetic friction forces
Fk = μk * N
N: Normal forces
Magnitude of moment
Force x distance
= F x d = M * (L/T^2) * L = M * (L^2) * (T^-2)
d: Shortest distance between center of rotation and line of action force. d is perpendicular to the line of action of the force.
Pythagoras
a^2 + b^2 = c^2
Sine
Opposite/Hypotenuse Sinα = a/c a = Sinα * c c = a/Sinα α = sin^-1 * (a/c) β = sin^-1 * (b/c)
Cosine
Adjacent/Hypotenuse cosα = b/c b = cosα * c c = b/cosα α = cos^-1 * (b/c) β = cos^-1 * (a/c)
Tangent
Opposite/Adjacent tanα = a/b a = tanα * b b = a/tanα α = tan^-1 * (a/b) β = tan^-1 * (b/a)
Law of sines (any triangle)
Sinα/a = Sinβ/b = Sinθ/c
Sinα/a = Sinβ/b b = sinβ * a/Sinα c = Sinθ * b/Sinβ a = Sinα * c/Sinθ
Law of cosines (any triangle)
If two sides and the angle between them is known
c^2=a^2+b^2-(2ab)cosθ
Adding vectors
C(vector) = A(vector) + B(vector) =
(Ax + Bx) + (Ay + By) =
(Acosα i(vector) + Bcosβ i(vector)) + (Asinα j(vector) + Bsinβ j(vector))
C(vector) = (Acosα + Bcosβ)i(vector) + (Asinα + Bsinβ)j(vector)
Linear Function
Y = f(X) = 1+2X f(X) = a+bX
