Reading...
Play button
Play button
Use LEFT and RIGHT arrow keys to navigate between flashcards;
Use UP and DOWN arrow keys to flip the card;
H to show hint;
A reads text to speech;
33 Cards in this Set
- Front
- Back
|
Cyl e-r
|
cos(T) i + sin(T) j
|
|
|
Cyl e-theta
|
-sin(T) i + cos(T) j
|
|
|
e-tang
|
cos(P)i+sin(P)j
|
|
|
e-norm
|
-sin(P)i+cos(P)j
|
|
|
Sph e-r
|
sin(P)cos(T)i + sin(P)sin(T)j + cos(P)k
|
|
|
Sph e-phi
|
cos(P)cos(T)i+cos(P)sin(T)j-sin(P)k
|
|
|
Sph e-theta
|
-sin(T)+cos(T)j
|
|
|
Primative Variables
(Definition) |
Variables which can be explained but not defined
|
|
|
Primative Variables (4)
|
Space, Time, Mass, Force
|
|
|
Defined Variables(3)
|
Position, Velocity, Acceleration
|
|
|
Axioms Definition
|
Statements based on observations, not proofs. These are based on variables.
|
|
|
Newton's 1st law/axiom
|
In an inertial dreference frame, if the sum of forces acting on a particle (∑F) is zero, the particle is at rest, or in a state of uniform velocity.
Note: Inertial reference frame- a box on the floor isn’t technically “moving” even though the earth is spinning. It all depends on how you define your “frame”. |
|
|
Newton's 2nd law/axiom
|
In an inertial reference, frame, if the sum of forces acting on a particle is not zero (∑F≠0), the sum of the forces (∑F) is proportional to the time rate of change of momentum (mv ⃗_P ) of the particle
Note: Integrate mv and you get m∙a (force) (F=ma) |
|
|
Newton's 3rd law/axiom
|
3. In an inertial reference frame, the interaction between any two (2) particles is through a pair of forces equal in magnitude, opposite in direction, and act along the straight long joining the two (2) particles.
Note: For every action, there is an equal and opposite reaction. |
|
|
K
|
constant in newton's 2nd law which takes into account variation in units
|
|
|
Steps to solving a problem
|
1. Define a Coord system
2. In motion diagram 3. FBD |
|
|
w (omega)
|
sqrt(k/m)
|
|
|
Use this equation to help solve for homogeneous linear equations
|
x=Ae^lamba(t)
|
|
|
Sph X
|
rsin(P)cos(T)
|
|
|
Sph Y
|
rsin(P)sin(T)
|
|
|
Sph Z
|
rcos(P)
|
|
|
System of Particle Applications
|
1. Rigid Body Dynamics
2. Deformable Body Dynamics 3. Fluid Dynamics 4. Fluids 5. Control 6. Combustion |
|
|
Potential Energy
|
U=mgh
|
|
|
Kinetic Energy
|
K=1/2 mv^2
|
|
|
Spring Force
|
kx
|
|
|
Centripetal Force
|
(mv^2)/R
|
|
|
Radius of Curvature
|
P
|
|
|
Curvature
|
d(T)/ds
|
|
|
Cyl Vp
|
R(dot) e-r + r(thetadot) e-theta + zdot k
|
|
|
Cyl Ap
|
[R(dbldot)-r(thetadot)^2]e-r + [2(rdot)thetadot+r(thetadbldot)] e-theta + zdbldot k
|
|
|
Tan Vp
|
sdot(e-t)
|
|
|
Tan Ap
|
sdbldot(e-t)+((sdot)^2)/p (e-n)
|
|
|
sphr Vp
|
rdot (e-r) +r(thetadot)sin(P) (e-theta) + r(phidot)(e-phi)
|
