Vector Rules

A . B = A

A x B = (A

_{x }B_{x }+ A_{y }B_{y }+ A_{z }B_{z}A x B = (A

_{y }B_{ z }- A_{z }- B_{y }) î - (A_{x }B_{ z }- A_{z }- B_{x }) ĵ
More information on vectors available in the Introduction to Vectors and Calculus page as well as the Introduction to Linear Algebra page.

Positional equations

if a

v

x

v

_{x}is a constant acceleration then the movement for some object is governed by:v

_{x }= v_{x0 }+ a_{x }tx

_{0 }= x_{0 }+ v_{x0 }t + 1/2 a_{x0 }t^{2 }v

^{2 }_{x }= v^{2 }_{x0 }+ 2 a_{x }t (x- x_{0 })
if a non-constant:

v (t) = v

x (t) = x

This is basically the same result as before, we are just integrating over a time dependent acceleration and velocity, so we take the areas under these curves to find the velocity.

_{0 }+ ∫ a(t') dt'x (t) = x

_{0 }+ ∫ v(t') dt'This is basically the same result as before, we are just integrating over a time dependent acceleration and velocity, so we take the areas under these curves to find the velocity.

Momentum and Energy

p = m v

Kinetic - m v

Potential due to gravity on earth - m g h

The most important aspect of this is that the total momentum in a closed system or frame is conserved. This is the famous conservation of momentum law, or newton's second law in its more complete form.

Kinetic - m v

^{2 }/ 2Potential due to gravity on earth - m g h

The most important aspect of this is that the total momentum in a closed system or frame is conserved. This is the famous conservation of momentum law, or newton's second law in its more complete form.

Force

F = m a

F = dp/dt = m dv/dt + v dm/dt

F = dp/dt = m dv/dt + v dm/dt

Gravitation

g = 9.8 m/s^2

approximate acceleration due to gravity on earth

G = 6.7 x 10^-11 N m^2/kg^2

Gravitational constant

approximate acceleration due to gravity on earth

G = 6.7 x 10^-11 N m^2/kg^2

Gravitational constant

F = -(G M

U = -(G M

_{1 }M_{2 })/R_{12}U = -(G M

_{1 }M_{2 })/R^{2}_{12}
Frictional Force

F

F

_{fric }= μ F_{Norm}F

_{Norm}is the normal force, which is perpendicular to the direction of movement.
Parameter Relations

F = - dU/dx

W = ∫ F . ds

P = dE/dt = F . v

J = ∫ F dt = Δ p

W = ∫ F . ds

P = dE/dt = F . v

J = ∫ F dt = Δ p

Center of mass

R

I = Σ m

_{cm }= Σ m_{i}R_{i}/ Σ m_{i}I = Σ m

_{i }R^{2 }_{i}
Rotational Motion

if α is constant

ω = ω

θ = θ

ω

ω = ω

_{0 }+ α tθ = θ

_{0 }+ ω t + 1/2 α t^{2 }ω

^{2 }= ω^{2 }_{0 }+ 2 α (θ - θ_{0 })
Combined Rotational and Non-Rotational kinetic energy

K = 1/2 I ω

^{2 }+ 1/2 m v^{2}
τ = r x F

L = r x p

τ = dL/dt

τ = I α

L = I ω

W = ∫ τ d θ

L = r x p

τ = dL/dt

τ = I α

L = I ω

W = ∫ τ d θ

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