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Bixel AP Physics > AP Electricity and Magnetism Equations to memorize > Flashcards

AP Electricity and Magnetism Equations to memorize Flashcards

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AP® Physics flashcards Physics 101 flashcards
1
Q

Rotational instantaneous power

A

P = τ·ω

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1
Q

Electric field of a point charge

A

E = kq / r2

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1
Q

Ampere’s law

A

μ0I = ∫(B)(ds)

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2
Q

Integral of a differential

A

∫ dx = x + C

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3
Q

Centripetal acceleration based upon v

A

ac = v2 / r

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3
Q

Lenz’s law

A

The current induced by a changing magnetic flux creates a field which opposes the change

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4
Q

Energy in an inductor

A
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5
Q
A
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6
Q

Newton’s third law

A

Fab = -Fba

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6
Q

Impulse for a constant force

A

J = (ΣF)(Δt)

(Impulse = force x time)

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6
Q

Area under a force/time function

A

Impulse

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6
Q

Instantaneous power

A

P = F∙v

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6
Q

Energy in a capacitor (3)

A

U = ½QV = ½CV2 = ½Q2/C

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7
Q

Derivative chain rule

A

d/dx (u) = (du / dv)(dv / dx)

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8
Q

Resistors in series

A

Rseries­ = R1 + R2 + R3 ….

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9
Q

Spring force

A

Fsp = -ks

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9
Q

Derivative quotient rule

A

d/dx (u / v) = (1/v)(du/dx) – (u/v2)(dv/dx)

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11
Q

Relative motion

A

va,c = va,b + vb,c

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11
Q

Center of mass

A

rcm = (m1)(r1) + (m2)(r2) … / Σm

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11
Q

Rule for the angle of the cross product

A

Rotate counterclockwise from the first vector to the second vector

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12
Q

Conservation of angular momentum

A

I1ω1 = I2ω2

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13
Q

Centripetal acceleration based upon ω

A

ac = ω2R

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14
Q

Relationship between the force and the change in energy per unit distance.

A

F = -dU/ds

This is a combination W = f x d and W = -ΔU

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15
Q

Work – potential energy relationship

A

-W = ΔU

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15
Q

Resistance of a wire

A

R = ρ(L/A)

Where ρ is resisitivity

L = length

A = cross sectional area

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15
Q

Magnetic field of a straight wire

A

B = μ0I / 2πR

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17
Q

vf2 equation

A

vf2 = vi2 + 2(a)(Δs)

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17
Q

Force down an incline

A

Fll = Fg ∙ sinθ

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17
Q

Gravitational potential energy on a planet

A

Ug = mgh

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17
Q

Rotational inertia of point masses

A

I = Σ(mr2)

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18
Q

Slope of a velocity/time graph

A

Acceleration

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18
Q

Torque (2)

A

τ = F∙ r┴

( torque = force times “lever arm” )

(The lever arm is just the shortest distance between the axis of rotation and the path the force is acting along.)

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19
Q

Cartesian to polar coordinates (2)

A

v = √(vx2 + vy2)

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20
Q

Rotational work

A

Wrot­ = (τ)(Δθ)

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21
Q

Integral of an exponential term

A

∫ (eu)dx = (1/u’)(eu) + C

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23
Q

Describe the electric field inside a conductor

A

Electric charge and field are zero

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23
Q

Voltage across an inductor

A

V = -L(dI / dt)

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24
Q

Battery emf

A

EMF = V - IRint

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25
Q

Magnetic flux

A

ФB = A∙B = ABcosθ

(Often, in the problems we do, the area vector and the magnetic field will be parallel, so the cosθ is equal to one and thus dropped from the equation.)

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26
Q

Resistors in parallel

A

1/Rparallel = 1/R1 + 1/R2 + 1/R3….

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28
Q

Centripetal force

A

Fc = mac

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28
Q

Period of a simple pendulum

A

T = 2π√(L/g)

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30
Q

Kinetic friction

A

Fkf = ± μkf∙ FN

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30
Q

Integrating with a constant

A

∫ k f(x)dx = k ∫ f(x)dx

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32
Q

Period of a physical pendulum

A

T = 2π√(I/mgd)

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33
Q

Power in a circuit (3)

A

P = IΔV

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35
Q

Electric potential (general)

A

V = U / q

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36
Q

Displacement under constant acceleration

A

Δs = (vi)(Δt) + ½(a)(Δt2)

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36
Q

Electrostatic force between point charges

A

FE = kq1q2 / r2

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37
Q

Acceleration due to gravity

A

g = G∙mp/rp2

(This is pretty much just the Law of Universal Gravitation with the mass of the planet and the radius of the planet plugged in.)

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38
Q

RC circuit growth

A

Vc = Vs(1e-t / RC)

RC the time constant (tau) (resistance x capacitance)

Vs is the supplied voltage

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39
Q

Law of Biot-Savart

A
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40
Q

Gravitational potential energy in space

A

Ug = (-G∙m1∙m2)/ r

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41
Q

Universal force of gravity

A

Fg = (G∙m1∙m2 )/ r2

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42
Q

Acceleration

A

a = dv / dt

43
Q

Slope of a potential energy / position graph

A

Negative of force

45
Q

Power input by a force

A

P = W / Δt

46
Q

Electric flux

A

ФB = E∙A

( In most cases that we will work with at this level, the two will be perpendicular, so the dot product just drops out. )

48
Q

Area under an acceleration/time function

A

Change in velocity

49
Q

Sum rule for integration

A

∫ (u + v)dx = ∫ (u)dx + ∫ (v)dx + C

50
Q

Derivative of sin

A

d/dx (sin x) = cos x

51
Q

Area under a force/position function

A

Work

52
Q

Escape velocity

A

v = √2Gm / R

53
Q

Kinetic energy

A

K = ½ mv2

53
Q

Inductance

A
54
Q

Constant acceleration

A

a = Δv / Δt

55
Q

Derivative of cos

A

d/dx (cos x) = - sin x

57
Q

Derivative of exponential terms

A
59
Q

RH open palm rule for force on a moving charge

A

Thumb - direction charge or current is moving

Fingers - direction of magnetic field

Open palm - direction of force.

60
Q

Displacement

A

Δs = sf – si

60
Q

Potential energy in a spring

A

Usp= ½ ks2

62
Q

Force between two wires

A
63
Q

Integral of sin

A

∫ (sin x)dx = -cos x + C

64
Q

Horizontal vector component

A

vx = v(cos θ)

65
Q

Formula for finding initial vertical velocity of a projectile given its initial velocity and angle at which it is fired.

A

vy = v(sin θ)

66
Q

Capacitance (2)

A

C = ε(A/d)

ε = permeativity of free space (8.85 x 10-12 F/m)

67
Q

Relationship between electric potential and electric field.

A

dV = -E·ds

68
Q

Force in a gravitational field

A

Fg = -mg

69
Q

Power rule for integration

A

∫ f(xn)dx = (xn+1/n+1) + C

70
Q

Conservation of angular momentum

A

ΔL=0

if and only if

Στext = 0

71
Q

Faraday’s law of induction

A

EMF = -N(dФB / dt)

( N is the number of loops )

72
Q

Rule for the angle of the dot product

A

Rotate counterclockwise from the first vector to the second vector

73
Q

Work done by a variable force

A

W = ∫(F)(ds)

74
Q

Newton’s second law for rotation

A

Στ = I∙α

( α is alpha, or angular acceleration )

76
Q

Momentum

A

p = mv

78
Q

Rotational kinetic energy

A

Krot = ½∙I∙ω2

79
Q

Magnetic force on current-carrying wire

A

F = IL x B

81
Q

Integrating 1/x

A

∫ (1/x)dx = ln|x| + C

82
Q

Angular momentum (2)

A

L = rmv

also

L = Iω

83
Q

Impulse equation

A

J = Δp

( Impulse = change in momentum )

84
Q

Satellite velocity

A

vsat = √(G∙mcenteral / rorbit)

86
Q

Slope of a momentum/time graph

A

Force

87
Q

Derivative sum rule

A

d/dx (u + v) = du/dx + dv/dx

88
Q

Relationship between period and frequency

A

T = 1/f

90
Q

RC circuit decay

A

Vc = Vi(e-t / RC)

RC the time constant (tau) (resistance x capacitance)

Vi is the intital voltage on the capacitor

91
Q

Static friction

A

Fsf ≤ ± μsf ∙ FN

92
Q

Integral of cos

A

∫ (cos x)dx = sin x + C

93
Q

Work (2)

A

W = (Fll)(Δs)

95
Q

Work – energy theorem

A

ΣW = ΔK

( make sure you remember this one )

96
Q

Velocity

A

v = ds / dt

98
Q

Gravitational field lines

A

Vectors point how a test mass would accelerate

99
Q

Electric current

A

I = dQ / dt

100
Q

Parallel axis theorem

A

I = Icm + md2

( If you know the moment of interia of an object rotating around its center of mass Icm but the object is instead rotating around an axis that is distance “d” from the center of mass, the new rotational intertia can be found with this equation )

101
Q

Average velocity

A

vavg = Δs / Δt

102
Q

Area under a velocity/time function

A

Change in position

103
Q

Conservation of energy

A

ΣU + ΣK + ΣEth = constant for a closed system

( this is a simplification, as it does not include chemical potential energy, electrical potential energy, etc. )

104
Q

Derivative power rule

A
105
Q

Period of a spring oscillator

A

T = 2π√(m/k)

106
Q

RL circuit decay

A

VL = V0(e-Rt / L)

108
Q

Magnetic force on a moving charge

A

F = qv x B

109
Q

Speed

A

S = distance / time

110
Q

Kirchhoff’s rule

A

ΔVloop = 0

112
Q

Capacitance with a dielectric

A

C = κε(A/d)

κ = dielectric constant

113
Q

Impulse for a variable force

A

J = ∫(F)(dt)

114
Q

Gauss’s law for permanent magnets

A

ФB = 0

115
Q

Newton’s second law

A

ΣF = ma

(don’t forget how many times you could get 1 point on a free response simply by writing this down)

116
Q

Angular frequency (2)

A

ω = 2πf

117
Q

Slope of a position/time graph

A

Velocity

118
Q

Average velocity when acceleration is constant

A

vavg = (vi + vf ) / 2

119
Q

Ohm’s law

A

ΔV = IR

120
Q

Force perpendicular to an incline

A

FN = Fg ∙ cosθ

121
Q

Electrostatic potential energy of two point charges

A

UE = kq1q2 / r

122
Q

Electric field (general)

A

E = F / q

123
Q

Capacitors in series

A

1/Cseries­ = 1/C1 + 1/C2 + ….

124
Q

Electric potential of a point charge

A

V = kq1 / r

125
Q

Conservation of momentum

A

Σpi = Σpf if ΣFext = 0

( With no external forces, the momentum of a system will be conserved )

( This is true for both linear and angular momentum )

126
Q

Electric field lines

A

Vectors pointed how a positive test charge would accelerate

127
Q

Power (general)

A

P = ΔE / Δt

128
Q

Capacitors in parallel

A

Cparallel= C1 + C2 + C3 ….

(Note: this is sort of opposite the rule for resistors in parallel. )

130
Q

Derivative product rule

A

d/dx (uv) = v(du/dx) + u(dv/dx)

131
Q

RH curl rule for a wire’s magnetic field

A

Point RH thumb in the direction of the current, RH fingers curl in the direction of the resulting magnetic field.

132
Q

Rotational inertia of radially symmetric objects

A

I = kMR2

( k = the number of these objects )

133
Q

Gauss’s law

A

Qenc = ε0ФE

134
Q

Equations for rolling (3)

A

ds = r∙dθ

135
Q

Time constant for RC circuit

A

τ = RC

τ is tau

R = resistance

C = capacitance

136
Q
A

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