kinematics
v� = v? + at
v�� = v?� + 2a?x
?x = v?t + �at�
?x = v�t - �at�
?x = �(v� + v?)t
resultant
r = ?(x� + y�)
x vector
x = r(cos?)
y vector
y = r(sin?)
polar angle
? = tan?�(y/x)
work
W = F?x(cos?)
Newton's 1st law of motion
An object in motion will remain in motion indefinitely unless acted on by an outside force
***Inertia
Newton's 2nd law of motion
F = ma
***Most important mechanics equation
Newton's 3rd law of motion
For every action, there is an equal and opposite reaction
***Action-reaction pairs
force of gravity
F = (Gm?m?)/r�
force of friction
F = (�k)(Fn)
kinetic energy
KE = �mv�
work-energy theorem
w = ?KE
gravitational potential energy
?PE = - W = mgh
"W" is the work due to gravity
potential energy of a satellite
U = -(GMm)/r
kinetic energy of a satellite
K = (GMm)/2r
mechanical energy of a satellite
ME = -(GMm)/2r
conservation of total energy
ME? = ME?
power
P = W/t
momentum
p = mv
force
F = ?p/?t
impulse
J = ?p = F?t
conservation of linear momentum
p = p'
(mtotal)?(vtotal)? = (mtotal)?(vtotal)?
centripetal acceleration
ac = v�/r
***not an actual, physical quantity
centripetal force
Fc = (mv�)/r
***not an actual, physical quantity
center of mass
x = (m?x? + m?x? + ...)/(mtotal)
torque
t = rFsin?
r = distance from pivot to the force's point of application
angular velocity
? = ??/?t
angular acceleration
? = ??/?t
angular displacement
?? = ?s/r
s = r?
linear velocity
v = r?
linear acceleration
a = r?
angular centripetal acceleration
ac = ?�r
Kepler's 1st law
The orbit of each planet is an ellipse and the sun is at one focus
***Remember the length of the semimajor axis usually = the R value
Kepler's 2nd law
An imaginary line from the sun to a moving planet sweeps out equal areas
***This implies that the closer a satellite/planet gets to the sun/planet, the faster its orbit becomes (so it can cover the same area as it would farther away, in the same amount of time).
Kepler's 3rd law
(T?)�/(T?)� = (R?)�/(R?)�
The ratio of the square of a planet's period of revolution (the time for one complete orbit) to the cube of its average distance from the sun is a constant that is the same for all planets.
Coulomb's law
|F| = (k|q?q?|)/r
electric field
E = F/q
electric field
E = V/d
electric field
E = (kq)/r�
important fact
There can be no electric field within the body of a conductor
electric potential energy
?U = -W
W = work applied by electric force
electric potential difference
?V = ?U/q
electric potential (voltage)
V = (kq)/r
capacitance
C = q/?V
capacitance
C = (??A)/d
parallel capacitance
C? = C?+C?
series capacitance
1/C? = 1/C? + 1/C?
dielectric
Increases the capacitance of a capacitor
***Is often an insulator
current
I = ?q/?t
resistance
R = ?V/I
power
P = IV
P = I�R
P = V�/R
series resistance
R? = R? + R?
parallel current
I? = I? + I?
series current
I? = I? = I?
parallel resistance
1/R? = 1/R? + 1/R?
magnetic force
F = |q|vBsin?
***F is the magnetic force, perpendicular to magnetic field
magnetic field rules
Magnetic force F is always perpendicular to both v and B
Magnetic forces cannot change the speed of an object, only its direction
The magnetic field does no work on any charge
magnetic force
F = I?Bsin?
? = length
EMF
? = B?v = ??/?t
flux
? = BAcos?
inverse
Electric PE vs. Capacitance
What is the relationship?
resistance
R = (?L)/A
***? is rho and is the variable for resistivity
important fact
Equivalent current, equivalent resistance, and equivalent voltage have to be found before ANY junction values in a circuit.