MCAT Physics Comprehensive

V_avg = (V₁ + V₂) / 2

Time to reach peak * average velocity

Total time in air * X component of V_initial

No acceleration. Can however have velocity but a = 0

Yes

Has both magnitude and direction.

Has only magnitude

The velocity of a body remains constant unless the body is acted upon by an external force.

F=ma

For every action there is an equal and opposite reaction.

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

C_mass = (r₁m₁ + r₂m₂ + r₃m₃...)/m_total

r - the displacement vector between a reference point and each vector.

At the center of mass.

The geometric center, irrespective of the center of mass.

• No acceleration
• No NET force
• All forces sum to zero
• No change in direction
• The object is in equilibrium

Distance = rate * time

Range = V_x * time

• Horizontal velocity never changes (ignoring wind resistance)
• Horizontal acceleration always = 0
• Vertical acceleration always = 10 m/s²
• 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.

X = 1/2at²

V = √(2gh)

t_air = 2V/g

V must be the vertical component of initial velocity

Greater surface area = more air resistance

Less aerodynamic = more air resistance

Rough surface = more air resistance

Greater velocity = more air resistance

A field that exists between any two objects with mass.

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

(In space)

F = mg

(Near earth)

(In space)

PE = mgh

(Near earth)

• 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.

F_f = µ_(s/k)F_N

F_f = µ_(s/k)mgcos

F = mgsin

F_N = mgcos

V_f = √(2gh)

F = k∆x

• x - displacement
• k - spring constant

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

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

• T = F
• T = mg
• T = Frsin

• - lever arm
• r - distance between the force and the point of rotation.
• rsin - always equals , but r = only when = 90˚

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.

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.

• - angular frequency (rad/s)
• v - tangential velocity (m/s)
• r - radius (m)
• f - frequency (Hz)

For the MCAT angular frequency and angular velocity are synonymous.

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

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

• Impulse = ∆
• Impulse = m∆v
• Impulse = F_avgt

• If there is no change in velocity, there can be no impulse.
• The greater the change in velocity the greater the change in impulse.

• (KE₁ + KE₂)_before + (KE₁ + KE₂)_after
• In elastic collisions momentum and energy are both conserved.

m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂

In inelastic collisions momentum is conserved but energy is not. For perfectly inelastic collisions the equations becomes:

m₁v₁ + m₂v₂ = (m₁ + m₂)v₃

Force/Area

∆dimension/original dimension

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.

∆L = L_o∆T

• T - temperature
• L - length in inches
• - coefficient of thermal expansion

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

Energy dissipated as heat. On the MCAT this usually means heat dissipated from a collision.

Heat energy and internal energy are almost synonymous.

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

ME = KE + PE

• W = ∆Energy
• W = Fdcos

Units - Joules () or ()

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

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

The pressure difference between a system and the surrounding atmosphere.

• 760 torr
• 760 mmHg
• 101 kPa
• 101,000 Pa
• 14.7 psi

P = F/A

Pressure = Force / Area

P = gh

• (rho) = fluid density
• g = gravity
• h = height of fluid

SG = D_substance/D_H2O

D = density

• 1000 kg/m³
• 1.0 g/cm³

1cm³ = 1mL

1L = 1kg

1mL = 1gram

The ratio of the density of the object to the density of the liquid.

The buoyant force is exactly equal to the weight of the displaced fluid.

F_buoyant = vg

• = fluid density
• v = volume of displaced fluid
• g = gravity

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.

• Q = AV
• Q = flow
• A = cross-sectional area of tube (m²)
• V = velocity of the fluid (m/s)

Application (cardiac output = stroke volume x heart rate)

K = P + gh + 1/2 v2

• P = random kinetic energy of the fluid molecules
• gh = the gravitational potential energy of the fluid
• 1/2v² = the energy due to moving fluid molecules
• K = a constant

v = √(2gh)

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

An attraction between unlike particles.

An attraction between particles of the same kind.

e- = 1.6 E^-19 C

From positive (+) to negative (–)

From negative (–) to positive (+)

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).

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

Equates to "real" gravity or gravity in space.

Equate to "assumed" gravity or gravity near earth.

E - Strength of electric field

K - constant

r - radius or distance

q - charge

E = V/d

• E - strength of an electric field
• V - voltage
• d - distance

V = Kq/r

• V - voltage
• K - constant
• r - radius

V = PE/q

Voltage is equal to potential energy over charge

R = pL/A

• p - resistivity
• L - length
• A - cross-sectional area

U = 1/2 CV²

U - PE

C - capacitance

V - voltage

C = Q/V

Q - charge

• Insulator
• Polarizable
• Resistor
• Makes more charge build up on the plates

• Plate area (directly related)
• Plate thickness (no effect)
• Distance between plates (inversely related)
• Strength of dielectric (directly related)

• Positive terminal has highest electric potential.
• Electrons build up on negative terminal and move to positive.

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

• 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

V = IR

• V - voltage
• I - current
• R - resistance

P = IV

P - power

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

F = qvBsin

• F - force