Helpful Phys/Math Formulae!!

[Layra-chan]

If you think of a useful formula or law or equation or relation or constants or whatever might be helpful, post it (or a description of it) here, and I'll try to make an organized compendium.  

[Layra-chan]

Notation and Abbreviations:

When I say that a force is "pointing toward/at" an object from a source, I mean that the force is pushing away from the source in the direction of the ray going from the source to the object.

UNDER CONSTRUCTION  

[Layra-chan]

Mechanics



UNDER CONSTRUCTION  

[Layra-chan]

 

[Layra-chan]

QM

UNDER CONSTRUCTION  

[Layra-chan]

Maths Stuff

UNDER CONSTRUCTION  

[Aetherius Lamia]

Why not just go to Wikipedia for whatever you want to read about?

For example, saying:

Net Torque = Rotational Inertia * angular acceleration

Torque = radius * Force * sin(smaller angle between them)

only tells you so much. Whereas Wikipedia pages to Torque, Rotational Inertia, and Angular acceleration let you read far more in depth. We can't even type out integrals here.  

[nonameladyofsins]

Aetherius Lamia

Why not just go to Wikipedia for whatever you want to read about?

For example, saying:

Net Torque = Rotational Inertia * angular acceleration

Torque = radius * Force * sin(smaller angle between them)

only tells you so much. Whereas Wikipedia pages to Torque, Rotational Inertia, and Angular acceleration let you read far more in depth. We can't even type out integrals here.

We're thinking of posting useful formulae here so that people could find them when they need them really quickly. Wikipedia works too, but we want to be such a resource place as well. Still it's gonna take a while, so don't worry about it now, keep using wikipedia.  

[UF6]

The falling rate of a object.

D=(G)*(t)-1/2(G)*(t)^2

 

[UF6]

Steven Hawkings

The falling rate of a object.

D=(G)*(t)-1/2(G)*(t)^2

The rate of a falling about on Earth is 10m/sec or 32ft/sec.

It as 10m/sec but some sites or people say 9.8m/sec when not rounded.  

[UF6]

The gravitational force between two objects can be expressed by the following equation: F= GMm/d^2.


F is the gravitational force, G is a constant known as the universal constant of gravitation, M and m are the masses of each object, and d is the distance between them.  

[Layra-chan]

Hey guys, sorry about the delay. I've been swamped lately; no time for more than a couple minutes of free time for Gaia per day.
And I can't believe I completely forgot about kinematics!! I feel silly now.  

[Dave the lost]

Steven Hawkings

Steven Hawkings

The falling rate of a object.

D=(G)*(t)-1/2(G)*(t)^2

The rate of a falling about on Earth is 10m/sec or 32ft/sec.

It as 10m/sec but some sites or people say 9.8m/sec when not rounded.

Acceleration due to gravity is commonly rounded to 9.8m/s², not 10. Everyone has a calculator nowadays, so there's not even the excuse that 10 is easier to use in calculations than 9.8.

Also, note that it's acceleration due to gravity, not rate of falling or anything, which implies velocity, which is dependant upon time falling, etc, and as such has units of ms^-2, or m/s², not m/s.


Anyway, didn't see these here:
v=u+at
v²=u²+2as
s=ut+½at²  

[Aetherius Lamia]

Would it be copyright infringement to simply copy formulae from a textbook?

Arc length of a curve in space

S = integral from t1 to t2 of ||r'(t)||dt

Are we including basic principles, like:

Quote:

Acceleration vector: a(t) = v'(t) = r''(t) = <0, -g, 0>
Velocity vector: ∫a(t) = v(t) = r'(t) = <||vi||*cos(theta), ||vi||*sin(theta) - g*t, 0>
Position vector: ∫v(t) = r(t) = <||vi||*cos(theta)*t, ||vi||*sin(theta)*t - (1/2)gt^2, 0> + ri
Where "vi" denotes the v-initial vector and "ri" denotes the r-initial vector.

Ugh. Anyone know how to create the arrows signifying a vector, the double bars (any better than ||v||) to denote the magnitude of a vector, the hat used to signify the direction of a vector?

(Yeah. The MTSU Math department introduces vectors in what they call Calculus III. UGH.)  

[CodeLabMaster]

The amount of work a human heart does:

W = P*A + (A*d*v^2)/(2*g)

...where W is the work done by the heart, P is the average blood pressure, A is the volume of blood entering/exiting the heart during a period of time, d is the density of the blood, v is the velocity of the blood leaving the heart, and g is Earth's gravitation acceleration constant, about 9.8m/s^2.