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This guide is a compilation of about fifty of the most important physics formulas to know
for the SAT Subject test in physics. (Note that formulas are not given on the test.) Each
formula row contains a description of the variables or constants that make up the formula,
along with a brief explanation of the formula.
Kinematics
vave =
∆x
∆t
v (^) ave = average velocity ∆x = displacement ∆t = elapsed time
The definition of average ve- locity.
vave =
(vi + vf )
v (^) ave = average velocity v (^) i = initial velocity v (^) f = final velocity
Another definition of the av- erage velocity, which works when a is constant.
a =
∆v
∆t
a = acceleration ∆v = change in velocity ∆t = elapsed time
The definition of acceleration.
∆x = vi ∆t +
a(∆t) 2
∆x = displacement v (^) i = initial velocity ∆t = elapsed time a = acceleration
Use this formula when you don’t have v (^) f.
∆x = vf ∆t −
a(∆t) 2
∆x = displacement v (^) f = final velocity ∆t = elapsed time a = acceleration
Use this formula when you don’t have v (^) i.
Kinematics (continued)
vf 2 = v i^2 + 2a∆x
v (^) f = final velocity v (^) i = initial velocity a = acceleration ∆x = displacement
Use this formula when you don’t have ∆t.
Dynamics
F = ma
F = force m = mass a = acceleration
Newton’s Second Law. Here, F is the net force on the mass m.
W = mg
W = weight m = mass g = acceleration due to gravity
The weight of an object with mass m. This is really just Newton’s Second Law again.
f = μN
f = friction force μ = coefficient of friction N = normal force
The “Physics is Fun” equa- tion. Here, μ can be either the kinetic coefficient of fric- tion μ (^) k or the static coefficient of friction μ (^) s.
p = mv
p = momentum m = mass v = velocity
The definition of momentum. It is conserved (constant) if there are no external forces on a system.
Work, Energy, Power (continued)
W = ∆(KE) W^ = work done
KE = kinetic energy
The “work-energy” theorem: the work done by the net force on an object equals the change in kinetic energy of the object.
E = KE + PE
E = total energy KE = kinetic energy PE = potential energy
The definition of total (“me- chanical”) energy. If there is no friction, it is conserved (stays constant).
P =
W
∆t
P = power W = work ∆t = elapsed time
Power is the amount of work done per unit time (i.e., power is the rate at which work is done).
Circular Motion
a c =
v 2
r
a (^) c = centripetal acceleration v = velocity r = radius
The “centripetal” acceleration for an object moving around in a circle of radius r at veloc- ity v.
Fc =
mv 2
r
F (^) c = centripetal force m = mass v = velocity r = radius
The “centripetal” force that is needed to keep an object of mass m moving around in a circle of radius r at velocity v.
Circular Motion (continued)
v =
2 πr
T
v = velocity r = radius T = period
This formula gives the veloc- ity v of an object moving once around a circle of radius r in time T (the period).
f =
T
f = frequency T = period
The frequency is the number of times per second that an object moves around a circle.
Torques and Angular Momentum
τ = rF sin θ
or
τ = rF⊥
τ = torque r = distance (radius) F = force θ = angle between F and the lever arm F (^) ⊥ = perpendicular force
Torque is a force applied at a distance r from the axis of ro- tation. F (^) ⊥ = F sin θ is the component of F perpendicu- lar to the lever arm.
L = mvr
L = angular momentum m = mass v = velocity r = radius
Angular momentum is con- served (i.e., it stays constant) as long as there are no exter- nal torques.
Electric Fields and Forces (continued)
F = qE
F = electric force E = electric field q = charge
A charge q, when placed in an electric field E, will feel a force on it, given by this formula (q is sometimes called a “test” charge, since it tests the elec- tric field strength).
E = k
q
r 2
E = electric field k = a constant q = charge r = distance of separation
This formula gives the elec- tric field due to a charge q at a distance r from the charge. Unlike the “test” charge, the charge q here is actually gen- erating the electric field.
E =
V
d
E = electric field V = voltage d = distance
Between two large plates of metal separated by a distance d which are connected to a battery of voltage V , a uni- form electric field between the plates is set up, as given by this formula.
∆V =
W
q
∆V = potential difference W = work q = charge
The potential difference ∆V between two points (say, the terminals of a battery), is de- fined as the work per unit charge needed to move charge q from one point to the other.
Circuits
V = IR
V = voltage I = current R = resistance
“Ohm’s Law”. This law gives the relationship between the battery voltage V , the current I, and the resistance R in a circuit.
Circuits (continued)
P = IV
or
P = V 2 /R
or
P = I 2 R
P = power I = current V = voltage R = resistance
All of these power formulas are equivalent and give the power used in a circuit resistor R. Use the formula that has the quantities that you know.
R s =
R 1 + R 2 +...
R (^) s = total (series) resistance R 1 = first resistor R 2 = second resistor
...
When resistors are placed end to end, which is called “in se- ries”, the effective total resis- tance is just the sum of the in- dividual resistances.
R p
R 1
R 2
R (^) p = total (parallel) resistance R 1 = first resistor R 2 = second resistor
...
When resistors are placed side by side (or “in parallel”), the effective total resistance is the inverse of the sum of the re- ciprocals of the individual re- sistances (whew!).
q = CV
q = charge C = capacitance V = voltage
This formula is “Ohm’s Law” for capacitors. Here, C is a number specific to the capac- itor (like R for resistors), q is the charge on one side of the capacitor, and V is the volt- age across the capacitor.
Waves and Optics (continued)
n 1 sin θ 1 = n 2 sin θ 2
n 1 = incident index θ 1 = incident angle n 2 = refracted index θ 2 = refracted angle
“Snell’s Law”. When light moves from one medium (say, air) to another (say, glass) with a different index of re- fraction n, it changes direc- tion (refracts). The angles are taken from the normal (per- pendicular).
d o
d i
f
d (^) o = object distance d (^) i = image distance f = focal length
This formula works for lenses and mirrors, and relates the focal length, object distance, and image distance.
m = −
d i
d o
m = magnification d (^) i = image distance d (^) o = object distance
The magnification m is how much bigger (|m| > 1) or smaller (|m| < 1) the image is compared to the object. If m < 0, the image is inverted compared to the object.
Heat and Thermodynamics
Q = mc ∆T
Q = heat added or removed m = mass of substance c = specific heat ∆T = change in temperature
The specific heat c for a sub- stance gives the heat needed to raise the temperature of a mass m of that substance by ∆T degrees. If ∆T < 0, the formula gives the heat that has to be removed to lower the temperature.
Heat and Thermodynamics (continued)
Q = ml
Q = heat added or removed m = mass of substance l = specific heat of transformation
When a substance undergoes a change of phase (for exam- ple, when ice melts), the tem- perature doesn’t change; how- ever, heat has to be added (ice melting) or removed (water freezing). The specific heat of transformation l is different for each substance.
∆U = Q − W
∆U = change in internal energy Q = heat added W = work done by the system
The “first law of thermody- namics”. The change in inter- nal energy of a system is the heat added minus the work done by the system.
E eng =
W
Q hot
× 100
E (^) eng = % efficiency of the heat engine W = work done by the engine Q (^) hot = heat absorbed by the engine
A heat engine essentially con- verts heat into work. The engine does work by absorb- ing heat from a hot reservoir and discarding some heat to a cold reservoir. The formula gives the quality (“efficiency”) of the engine.
Pressure and Gases
P =
F
A
P = pressure F = force A = area
The definition of pressure. P is a force per unit area exerted by a gas or fluid on the walls of the container.
