ABSTRACT
Force = mass × acceleration F = ma N Weight = mass × gravitational field W = mg N
Centripetal acceleration a = v 2
r m/s2
Centripetal force F = mv 2
r N
Work done = force × distance moved W = Fs J
Efficiency = useful output energy input energy
Power = energy used (or work done) time taken
= force × velocity P = E t
= Fv W
Potential energy = weight × change in height Ep = mgh J
Kinetic energy = 1 2
× mass× (speed)2 Ek = 1 2
mv2 J
Moment = force × perpendicular distance M = Fd N m
Angular velocity ω = θ t
= 2πn rad/s
Linear velocity v = ωr m/s Relationships between initial velocity u, final velocity v, displacement s, time t and constant acceleration a
⎧ ⎪⎨
⎪⎩ s = ut + 1
2 at2
v2 = u2 + 2as
m
(m/s)2
Relationships between initial angular velocity ω1, final angular velocity ω2, angle θ , time t and angular acceleration α
⎧ ⎪⎨
⎪⎩ θ = ω1t +
1 2 αt2
ω22 = ω21 + 2αθ
rad
(rad/s)2
Frictional force = coefficient of friction × normal force F = μN N
Force ratio = load effort
Formula
Movement ratio = moved by effort distance moved by load
Efficiency = force ratio movement ratio
Stress = applied force cross-sectional area
σ = F A
Pa
Strain = change in length original length
ε = x L
Young’s modulus of elasticity = stress strain
E = σ ε
Pa
Stiffness = force extension
N/m
Momentum = mass × velocity kg m/s Impulse = applied force × time = change in momentum kg m/s Torque = force × perpendicular distance T = Fd N m Power = torque × angular velocity P = Tω = 2πnT W Torque = moment of inertia × angular acceleration T = Iα N m
Pressure = force area
p = F A
Pa
Pressure = density × gravitational acceleration × height p = ρgh Pa 1 bar = 105Pa Absolute pressure = gauge pressure + atmospheric pressure Quantity of heat energy = mass × specific heat capacity
× change in temperature Q = mc(t2 − t1) J
Kelvin temperature = degrees Celsius + 273 New length = original length + expansion L2 = L1[1 + α(t2 − t1)] m New surface area = original surface area + increase in area A2 = A1[1 + β(t2 − t1)] m2 New volume = original volume + increase in volume V2 = V1[1 + γ (t2 − t1)] m3
Characteristic gas equation p1V1 T1
= p2V2 T2
= k
pV = mRT
Formula Formula symbols Units
Charge = current × time Q = It C
Resistance = potential difference current
R = V I
Electrical power = potential difference × current P = VI = I2R = V 2
R W
Terminal p.d. = source e.m.f. − (current)(resistance) V = E − Ir V
Resistance = resistivity × length of conductor cross-sectional area
R = ρl A
Total resistance of resistors in series R = R1 + R2 + · · ·
Total resistance of resistors in parallel 1 R
= 1 R1
+ 1 R2
+ · · ·
Magnetic flux density = magnetic flux area
B = A
T
Force on conductor = flux density × current × length of conductor
F = BIl N
Force on a charge = charge × velocity × flux density F = QvB N Induced e.m.f. = flux density × current × conductor velocity E = Blv V
Induced e.m.f. = number of coil turns × rate of change of flux E = −N d dt
V
Induced e.m.f. = inductance × rate of change of current E = −L dI dt
V
Inductance = number of coil turns × flux current
L = N I
H
Mutually induced e.m.f E2 = −M dI1 dt
V
For an ideal transformer V1 V2
= N1 N2
= I2 I1
Electric field strength = p.d. across dielectric thickness of dielectric
E = V d
V/m
Electric flux density = charge area
D = Q A
C/m2
Formula
Charge = difference Q =
Parallel plate C = d
Total capacitance of capacitors in series: 1 C
= 1 C1
+ 1 C2
+ · · ·
Total capacitance of capacitors in parallel: C = C1 + C2 + · · · F
Energy stored in capacitor W = 1 2
CV 2 J
Wheatstone bridge Rx = R2R3
R1
Potentiometer E2 = E1 (
l2 l1
) V
Periodic time T = 1f s
r.m.s. current I = √√√√ i
2 1 + i22 + · · · + i2n
n A
For a sine wave
Average or mean value IAV = 2 π
Im
r.m.s. value I = 1√ 2
Im
Form factor = r.m.s. average
Peak factor = maximum r.m.s.
