Vectors Flashcards
Give the formula for velocity in terms of angular velocity and tragectory.
angular velocity X position = velocity
differential of trajectory = velocity
Give the formula for acceleration
differential of velocity = acceleration
Give the formula for momentum
mass (scalar) X velocity
Give the formula for angular momentum
trajectory X momentum = angular momentum
Give the formula for momentum (of Force)
Trajectory X Force = Momentum (of Force)
Give the formula for Force
mass (scalar) X acceleration = Force
How to find the ∇f of a function f(x,y)
For the x, y and potential z co-ordinate you have to partially differentiate the function with respect to each direction (d/dx, d/dy, d/dz)
How to find the directional derivative
First find the directional vector by multiplying the direction given by the inverse of the absolute value of the magititude (of the direction). The directional derivative is then solved by the dot product of the ∇f of a function by the directional derivative.
Divergence of a vector
partial(d/dx + d/dy + d/dz) of a vector
Curl of a vector
partial(d/dx + d/dy + d/dz) X the vector (meaning that for example d/dy X the j term would equal 0 whilst d/dz X the j term would give the negative i term as a partial derivative of the j term).
Explain the notations ∇ .∇f and ∇ X ∇f
∇ .∇f = divergence but using second order differentials
∇ X ∇f = curl but using second order differentials
How to find the material derivative D/DT
D/DT = partial d/dt + u.∇
where u = velocity field
For steady state flows what does this mean?
partial d/dt = 0
How do you integrate a ∇ term?
Find the terms that are common (that belong to the same variable but were differentiated with respect to x,y or z) if there are any. Then integrate all those terms.
How to determine if a vector (e.g: u) is irrotational
∇ X u = 0
