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MCAT Quicksheets > Physics and Math > Flashcards

Physics and Math Flashcards

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MCAT flashcards
1
Q

Vectors

A

Physical quantities with both magnitude and direction
Ex: force, velocity

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2
Q

Scalars

A

Physical quantities that have magnitude, but no direction
Ex: mass, speed

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3
Q

Average velocity

A

‘v’ = Δx / Δt

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4
Q

Acceleration

A

The rate of change of and object’s velocity
a = Δv / Δt

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5
Q

Linear motion equations

A

v = vo + at
x = vo(t) + 1/2a(t^2)
v^2 = (vo)^2 + 2ax
‘v’ = (vo + v) / 2
x = ‘v’t = ( (vo + v) / 2)t

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6
Q

Vertical component of velocity

A

v = vsinθ

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7
Q

Horizontal component of velocity

A

v = vcosθ

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8
Q

Static friction

A

The force that must be overcome to set an object in motion
0 ≤ fs ≤ (µs)N

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9
Q

Kinetic friction

A

Opposes the motion of objects moving relative to each other
fk = (µk)N

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10
Q

Newton’s first law

A

A body in a state of motion or at rest will remain in that state unless acted upon by a net force

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11
Q

Newton’s second law

A

When a net force is applied to a body of mass m, the body will be accelerated in the same direction as the force applied to the mass.
F = ma

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12
Q

N =

A

kg(m) / s^2

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13
Q

Work

A

For a constant force F, acting on an object that moves a displacement of d, the work is W = Fdcosθ
For a force perpendicular to the displacement, W = 0

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14
Q

Joule =

A

N(m)

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15
Q

Power

A

P = W / Δt

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16
Q

Kinetic energy

A

1/2mv^2

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17
Q

Newton’s third law

A

If body A exerts a force on body B, then B will exert a force back onto A that is equal in magnitude and opposite in direction
Fb = -Fa

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18
Q

Newton’s law of gravitation

A

All forms of matter experience an attractive force to other forms of matter in the universe
F = G(m1)(m2) / r^2

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19
Q

Mass vs weight

A

Mass: a scalar quantity that measures a body’s inertia
Weight (Fg): a vector quantity that measures a body’s gravitational attraction to the earth
Fg = mg

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20
Q

Uniform circular motion

A

ac = v^2 / r
Fc = mv^2 / r

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21
Q

Potential energy

A

U = mgh

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22
Q

Total mechanical energy

A

E = Pe + Ke
E = U + K

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23
Q

Work-energy theorem

A

Relates the work performed by all forces acting on a body in a particular time interval to the change in energy at that time
W = ΔE

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24
Q

Conservation of energy

A

When there are no nonconservative forces (such as friction) acting on a system, the total mechanical energy remains constant: ΔE = ΔK + ΔU = 0

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25
Q

Linear expansion

A

The increase in length by most solids when heated
*When temperature increases, the length of a solid increases “a Lot”
ΔL = αLΔT

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26
Q

Volume expansion

A

ΔV = βVΔT

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27
Q

Conduction

A

The direct transfer of energy via molecular collisions

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28
Q

Convection

A

The transfer of heat by the physical motion of a fluid

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29
Q

Radiation

A

The transfer of energy by electromagnetic waves

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30
Q

Specific heat

A

Q = mcΔT
- Can only be used when the object does not change phase
Q > 0 means heat is gained, and vise versa

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31
Q

Heat of transformation

A

The quantity of heat required to change the phase of 1g of a substance
Q = mL

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32
Q

First law of thermodynamics

A

ΔU = Q - W

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33
Q

Adiabatic

A

(Q = 0)
ΔU = -W

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34
Q

Constant volume

A

(W = 0)
ΔU = Q

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35
Q

Isothermal

A

(ΔU = 0)
Q = W

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36
Q

Second law of thermodynamics

A

In any thermodynamic process that moves from one state of equilibrium to another, the entropy of the system and environment together will either increase or remain unchanged

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37
Q

Density

A

(p) = m / V

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38
Q

Specific gravity

A

(p)substance / (p)water (no units)
(p)water = 10^3 kg / m^3

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39
Q

Weight

A

(p)gV

40
Q

Pressure

A

P = F / A
- For static fluids of uniform density in a sealed vessel, pressure = (p)gz
- Absolute pressure in a fluid due to gravity somewhere below the surface is given by the equation P = Po + (p)gz
- Gauge pressure:
Pg = P - Patm

41
Q

Continuity equation

A

A1v1 = A2v2

42
Q

Bernoulli’s equation

A

P + 1/2(p)v^2 + (p)gh = constant

43
Q

Archimedes’ principle

A

F(body) = (p)fluid (g) (Vsubmerged)

44
Q

Buoyant force

A

Equal to the weight of the displaced fluid
- If the weight of the fluid displaced is less than the object’s weight, the object will sink

45
Q

Pascal’s principle

A

A change in the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the containing vessel
P = F1 / A1 = F2 / A2
A1d1 = A2d2, so
W = F1d1 = F2d2

46
Q

Coulomb’s law

A

F = kq1q2 / r^2

47
Q

Electric field

A

E = Fe / q = kQ / r^2
- A positive point charge will move the same direction as the electric field vector; a negative charge will move in the opposite direction

48
Q

Electrical potential energy (U)

A

U = qΔV = qEd = kQq / r

49
Q

Electric dipoles

A

p is the dipole moment
(p = qd)

50
Q

Electrical potential

A

The amount of work required to move a positive test charge q from infinity to a particular point divided by the test charge
V = U / q

51
Q

Potential difference (voltage)

A

ΔV = W / q = kQ / r
- When two oppositely charged parallel plates are separated by a distance d, an electric field is created, and a potnetial difference exists between the plates, given by: V = Ed

52
Q

Current

A

The flow of electric charge
I = Q / Δt
- The direction of current is in the direction positive charge would flow, or from high to low potential

53
Q

Ohm’s law

A

V = IR (can be applied to circuit or individual resistors)

54
Q

Resistance

A

R = (p)L / A
- Resistance increases with increasing temperatures for most materials

55
Q

Kirchhoff’s laws

A
  1. At any junction within a circuit, the sum of current flowing into that point must equal the sum of current leaving
  2. The sum of voltage sources equals the sum of voltage drops around a closed-circuit loop
56
Q

Power dissipated by resistors

A

P = IV = V^2 / R = I^2(R)

57
Q

Capacitors

A

Capacitance: the ability to store charge per unit voltage
C = Q / V
C’ = (k) ((ε0)(A) / d)

58
Q

Series vs parallel C

A

Parallel = C + C
Series = 1/C + 1/C

59
Q

Energy stored by capacitors

A

U = 1/2QV = 1/2CV^2 = 1/2 Q^2 / C

60
Q

Wave formulas

A

f = 1 / T
v = f λ

61
Q

Standing waves (strings)

A

λ = 2L / n
f = nv / 2L
λ = 2L, λ = L, λ = 2L/3
*The ends of the strings are always nodes; nodes occur where the displacement is zero

62
Q

Open pipes

A

λ = 2L / n
f = nv / 2L
L = λ/2, L = λ, L = 3λ/2
*The open ends of the pipes are always antinodes (max amplitude

63
Q

Closed pipes

A

λ = 4L/n (n = odd 1, 3, 5)
f = nv / 4L
L = λ/4, L = 3λ/4, L = 5λ/4
*The closed end of a pipe is always a node, and the open end is always an antinode

64
Q

Sound

A

Propagates through deformable medium by the oscillation of particles parallel to the direction of the wave’s propagation

65
Q

Intensity

A

I = P / A

66
Q

Sound level

A

β = 10 log (I / I0)
Note: An increase of 10 dB is an increase in intensity by a factor of 10. An increase of 20 dB is an increase in intensity by a factor of 100

67
Q

Doppler effect

A

When a source and a detector move relative to one another, the perceived frequency of the sound recieved differs from the actual frequency emitted
f’ = f (v +- vD) / (v +- Vs)
Vs source
Vs dectector

68
Q

Refraction

A

n = c/v
c = 3.0 x 10^8 m/s

69
Q

Snell’s law

A

n1sinθ1 = n2sinθ2
- When n2 > n1, light bends toward the normal; when n2 < n1, light bends away from the normal

70
Q

Focal length

A

Mirrors:
(+) concave/converging
(-) convex/diverging
Lens:
(+) convex/converging
(-) concave/diverging

71
Q

Object distance (o)

A

Mirrors:
(+) real object (in front of mirror)
(-) virtual object (behind)
Lens:
(+) real object (in front of lens)
(-) virtual object (behind)

72
Q

Image distance (i)

A

Mirrors:
(+) real image (in front of mirror)
(-) virtual image (behind)
Lens:
(+) real image (behind lens)
(-) virtual image (in front of lens)

73
Q

Magnification (m)

A

Mirrors:
(+) upright image
(-) inverted image
Lens:
(+) upright image
(-) inverted image

74
Q

Converging systems

A
  1. o > 2f
    Real, inverted, reduced
  2. o = 2f
    Real, inverted, same
  3. 2f > o > f
    Real, inverted, magnified
  4. o = f
    No image
  5. o < f
    Virtual, upright, magnified
75
Q

Diverging systems

A

All o distances
Virtual, upright, reduced
(concave lens, convex mirro)
1/f = 1/o + 1/i

76
Q

Magnification

A

m = -i/o
P = 1/f (D = m^-1)

77
Q

Observer and detector moving closer:

A

+ sign in numerator
- sign in denominator

78
Q

Observer and detector moving apart:

A
  • sign in numerator
    + sign in denominator
79
Q

Photoelectric effect

A

E = hf = hc/λ
K = hf - W
K is the maximum kinetic energy of an ejected electron; W is the minimum energy required to eject an electron, called the work function

80
Q

Mass defect

A

Results from the conversion of matter to energy, embodied by:
E = mc^2 (this is the binding energy that holds nucleons within the nucleus)

81
Q

Half-life

A

n = noe^-λt

82
Q

Alpha decay

A

238/92 –> 234/90 + 4/2

83
Q

Beta-minus decay

A

137/55 –> 137/56 + 0/-1 + ‘v’e

84
Q

Beta-plus decay

A

22/11 –> 22/10 + 0/+1 + ve

85
Q

Gamma decay

A

12/6 –> 12/6 + 0/0Y

86
Q

Logarithmic identities

A
  1. log A x log B = log A + log B
  2. log A/B = log A = log B
  3. log A^B = Blog A
  4. log 1/A = -log A
87
Q

Converting logs

A

log x = ln x / 2.303
log (n x 10^m) ~ m + 0.n

88
Q

Scientific method

A

Determine whether sufficient background exists and whether the question is testable

89
Q

FINER method

A

Feasible, interesting, novel, ethical, and relevant

90
Q

Hill’s criteria

A

Help determine the strength of causal relationships; only temporality is necessary

91
Q

Error sources

A

Small sample size, defects in precision and accuracy, bias, confounding variables

92
Q

Ethics

A
  1. Beneficence: the requirement to do good
  2. Nonmaleficence: “do no harm”
  3. Autonomy: the right of individuals to make decisions for themselves
  4. Justice: the need to consider only morally relevant differences between patients and to distribute healthcare resources fairly
93
Q

Probability

A

Mutually exclusive: two events that cannot occur together
Independent: the probability of either event is not affected by the occurrence of the other

94
Q

Null hypothesis

A

A hypothesis of no difference; always the comparator

95
Q

p-value

A

The probability that results were obtained by chance given that the null hypothesis is true

96
Q

Confidence interval

A

A range of values believed to contain the true value with a given level of certainty

97
Q

Generalizability

A

Statistical significance and causality do not make something generalizable or a good intervention. Clinical significance and the target population must also be considered

MCAT Quicksheets (6 decks)

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