
Average velocity
V_{avg} = (V_{1} + V_{2}) / 2

Determining height reached
Time to reach peak * average velocity

Determining horizontal distance
Total time in air * X component of V_{initial}

Net force = 0 means...
No acceleration. Can however have velocity but a = 0

If volume changes, is work being done?
Yes


Vector attributes
Has both magnitude and direction.

Scalar attributes
Has only magnitude

Newton's first law
The velocity of a body remains constant unless the body is acted upon by an external force.


Newton's third law
For every action there is an equal and opposite reaction.

Inertia definition
The ability of an object to resist a change to its velocity.

Center of Mass formula
C_{mass} = (r_{1}m_{1} + r_{2}m_{2} + r_{3}m_{3}...)/m_{total }
r  the displacement vector between a reference point and each vector.

Center of gravity
At the center of mass.

Center of buoyancy
The geometric center, irrespective of the center of mass.

"Constant Velocity" or " Constant Speed" means
 No acceleration
 No NET force
 All forces sum to zero
 No change in direction
 The object is in equilibrium

Distance or height traveled formula
Distance = rate * time

Range (horizontal distance traveled) formula
Range = V_{x} * time

When facing projectiles think:
 Horizontal velocity never changes (ignoring wind resistance)
 Horizontal acceleration always = 0
 Vertical acceleration always = 10 m/s^{2}
 Vertical behavior is always symmetrical (upward = downward)
 Time in the air depends on the vertical component of velocity only.
 Range depends on both the vertical and horizontal components.
 Time is always the same for both the x and y components of the motion.

Formula for displacement in projectile motion
X = 1/2at^{2}

Formula for final velocity when only height is given
V = √(2gh)

Formula for "round trip" or total time in air
t_{air} = 2V/g
V must be the vertical component of initial velocity

The effect of surface area on air resistance
Greater surface area = more air resistance

The effect of shape on air resistance
Less aerodynamic = more air resistance

The effect of contour on air resistance
Rough surface = more air resistance

The effect of velocity on air resistance
Greater velocity = more air resistance

Gravity definition
A field that exists between any two objects with mass.

Field definition
An invisible influence that can exert a force on a mass or charge.

Universal Law of Gravitation (force due to gravity)
(In space)
F = mg
(Near earth)

Formula for gravity, strength of gravitational field, acceleration due to gravity

Gravitational Potential Energy
(In space)
PE = mgh
(Near earth)

Friction facts
 Friction opposes sliding not motion.
 If there is sliding, it's kinetic friction; if there's no sliding, it's static friction.
 Static µ is always greater than kinetic µ.
 Surface area does not increase friction when the mass is the same.

Force due to friction formula
F _{f} = µ _{(s/k)}F _{N}
F _{f} = µ _{(s/k)}mgcos

Force down an inclined plane formula
F = mgsin

Normal force on an inclined plane formula
F _{N} = mgcos

Velocity at the base of an inclined plane
V_{f} = √(2gh)

Hooke's Law
F = k∆x
 x  displacement
 k  spring constant

Elastic Potential Energy formula

Simple Harmonic Motion formulas
T = 2π√(m/k)
(mass on a spring)
T = 2π√(L/g)
(pendulum)
 T  period (time/wave)
 m  mass
 k  spring constant
 L  length of pendulum
 g  gravity

Equililbrium terms
 Terminal velocity
 Constant velocity
 Objects at rest
 Balanced fulcrums or boards on strings
 Objects floating in liquid


Solving for systems in and not in equilibrium
Equilibrium  list all the forces and put them equal to one another.
Not Equilibrium  list all the forces and add "ma" to the loosing side.


Centripetal vs. Centrifugal
If a string is pulling a ball into a circular motion, the string's force on the ball is centripetal and the ball's force on the string is centrifugal.
Centrifugal does not exist.


Rotational equilibrium
 An object is in rotational equilibrium if:
 1. It is NOT rotataing
 2. It is rotating with a constant angular velocity/frequency

Momentum
momentum is inertia increased by velocity and is always conserved (remains constant) in an isolated system.

Impulse
 Impulse = ∆
 Impulse = m∆v
 Impulse = F_{avg}t
 If there is no change in velocity, there can be no impulse.
 The greater the change in velocity the greater the change in impulse.

Elastic Collisions
 (KE_{1} + KE_{2})_{before} + (KE_{1} + KE_{2})_{after}
 In elastic collisions momentum and energy are both conserved.

Inelastic Collisions
m_{1}v_{1} + m_{2}v_{2} = m_{1}v_{1} + m_{2}v_{2 }
In inelastic collisions momentum is conserved but energy is not. For perfectly inelastic collisions the equations becomes:
m_{1}v_{1} + m_{2}v_{2} = (m_{1} + m_{2})v_{3}


Strain
∆dimension/original dimension

Modulus of elasticity (ME)
stress/strain
 Young's modulus  simultaneous pushing or pulling, perfectly lined up with one another.
 Shear modulus  simultaneous pushing or pulling not perfectly lined up.
 Bulk modulus  simultaneous compression from all sides.

Thermal expansion formula
∆L = L _{o}∆T
 T  temperature
 L  length in inches
  coefficient of thermal expansion

Internal energy
The energy of internal vibrations of molecules or atoms within a system.

Heat energy
Energy dissipated as heat. On the MCAT this usually means heat dissipated from a collision.
Heat energy and internal energy are almost synonymous.

Chemical energy
The energy contained within chemical bonds, or the energy stored/released due to the separation and/or flow of electrons.

Mechanical energy
ME = KE + PE

Work formulas
 W = ∆Energy
 W = Fdcos
Units  Joules ( ) or ( )

Atmospheric Pressure
Force per unit area exerted upon a surface by the weight of the air above that surface in the atmosphere.

Fluid Pressure
Force exerted by a fluid on a point equal to the density of the fluid times the depth.

Gauge Pressure
The pressure difference between a system and the surrounding atmosphere.

1 atm equivalents
 760 torr
 760 mmHg
 101 kPa
 101,000 Pa
 14.7 psi

General Pressure formula
P = F/A
Pressure = Force / Area

Fluid Pressure formula
P = gh
 (rho) = fluid density
 g = gravity
 h = height of fluid

Specific Gravity formula
SG = D_{substance}/D_{H}_{2O}
D = density

Density of water
 1000 kg/m^{3}
 1.0 g/cm^{3}

Volume measurements of water
1cm^{3} = 1mL

Mass of water
1L = 1kg
1mL = 1gram

For objects floating in fluid, the fraction submerged =
The ratio of the density of the object to the density of the liquid.

Archimede's Principle
The buoyant force is exactly equal to the weight of the displaced fluid.

Buoyancy formula
F_{buoyant} = vg
 = fluid density
 v = volume of displaced fluid
 g = gravity

Apparent Weight
The apparent weight of a submerged object is the actual weight minus the buoyant force.
The apparent weight gives us 1) the buoyant force and 2) the weight of that volume of fluid.

Flow Rate formula
 Q = AV
 Q = flow
 A = crosssectional area of tube (m^{2})
 V = velocity of the fluid (m/s)
Application (cardiac output = stroke volume x heart rate)

Bernoulli's Equation
K = P + gh + 1/2 v^{2
P = random kinetic energy of the fluid moleculesgh = the gravitational potential energy of the fluid1/2v2 = the energy due to moving fluid moleculesK = a constant
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Velocity of H_{2}O exiting a spigot formula
v = √(2gh)

Surface Tension
The intensity of intermolecular forces per unit length at the surface of a liquid.

Adhesion
An attraction between unlike particles.

Cohesion
An attraction between particles of the same kind.

Charge magnitude of an electron
e = 1.6 E^{19} C

Current flows...
From positive (+) to negative (–)

Electrons flow...
From negative (–) to positive (+)

What is current?
The flow of eletrons from areas of higher density (where they strongly repel each other) to areas of lower density (where there is less repulsion).

Electric Field
Field = an invisible influence that can exert a force on a mass or charge.

Point Charge Field
Equates to "real" gravity or gravity in space.

Constant Electric Field
Equate to "assumed" gravity or gravity near earth.

Electric field equivalent to "g" gravity
E  Strength of electric field

Electric field equivalent to "G" gravity constant
K  constant

Electric field equivalent to "h" height
r  radius or distance

Electric field equivalent to "m" inertial component
q  charge

Strength of an efield formula
E = V/d
 E  strength of an electric field
 V  voltage
 d  distance

Voltage for point charge efield formula
V = Kq/r
 V  voltage
 K  constant
 r  radius

Voltage formula
V = PE/q
Voltage is equal to potential energy over charge

Resistance formula
R = pL/A
 p  resistivity
 L  length
 A  crosssectional area

Capacitance formula
U = 1/2 CV^{2}
U  PE
C  capacitance
V  voltage
C = Q/V
Q  charge

Dielectric characteristics
 Insulator
 Polarizable
 Resistor
 Makes more charge build up on the plates

Variables that affect capacitance
 Plate area (directly related)
 Plate thickness (no effect)
 Distance between plates (inversely related)
 Strength of dielectric (directly related)

Capacitor charge vs. time graph

Conceptual ideas of a battery
 Positive terminal has highest electric potential.
 Electrons build up on negative terminal and move to positive.

Conceptual ideas of a resistor
 There is always a voltage drop across any resistor.
 Current through a resistor is inversely related to resistance. 2x resistance = 1/2 current.

Solving circuits
 Must be simplified, eg. no more than one of each component.
 1. Resistors in series: add directly
 2. Resistors in parallel: add the inverses and take the inverse
 3. Capacitors in series: add the inverses and take the inverse
 4. Capacitors in parallel: add directly
 5. Batteries in series: add directly
 6. Batteries in parallel: total voltage = the highest voltage of any one of the batteries in parallel

Ohm's Law
V = IR
 V  voltage
 I  current
 R  resistance

Electric power formula
P = IV
P  power

AC vs. DC
 Alternating current is created by a generator and can be represented by a sine wave.
 Direct current is created by a battery.

F_{magnet} on a charged particle formula
F = qvBsin

