Formula booklet understanding
Equation Unit Explanation
Uncertainties
If 𝑦 = 𝑎 ± 𝑏 Arbitrary → absolute uncertainty
Then: ∆𝑦 = ∆𝑎 + ∆𝑏
If 𝑦 =
𝑎𝑏 Arbitrary → fractional uncertainty
𝑐
∆𝑦 ∆𝑎 ∆𝑏 ∆𝑐
Then: 𝑦
= 𝑎
+ 𝑏
+ 𝑐
If 𝑦 = 𝑎^𝑛 Arbitrary → fractional uncertainty of which is equal
∆𝑦
Then 𝑦 = ||𝑛
∆𝑎 | to the fractional uncertainty of a^n
𝑎 | n = exponent of a (constant)
y:
a : measured value
Vectors & Scalars
𝐴 = 𝐴𝑠𝑖𝑛θ arbitrary Think of trigonometry → horizontal vector
ℎ
𝐴 = 𝐴𝑠𝑖𝑛θ arbitrary → vertical vector
𝑣
Motion
𝑣 = 𝑢 + 𝑎𝑡 metres/secon velocity
𝑣² = 𝑢² + 2𝑎𝑠 d
𝑠 = 𝑢𝑡 +
1
𝑎𝑡² metres displacement
2
(𝑣+𝑢)𝑡
𝑠= 2
Forces
𝐹 = 𝑚𝑎 Newtons Force exerted on object which is equal to
the mass times the acceleration of an
object
𝐹 ≤ µ 𝑠𝑅 Newtons Friction is equal or inferior to coefficient of
𝑓
friction times normal force for static object
𝐹 = µ 𝑅 Newtons Friction is equal to coefficient of friction
𝑓 𝑑
times normal force for dynamic object
Work, energy & power
𝑊 = 𝐹𝑠 𝐶𝑜𝑠θ Joules Work equal to the force times the
displacement times the cosine of the angle
of displacement
, 𝐸 =
1
𝑚𝑣² Joules Kinetic energy equal to half the mass of the
𝑘 2
object times the square of its velocity
𝐸 =
1
𝑘∆𝑥² Joules Potential energy equal to half the spring
𝑝 2
constant times the difference of x square
∆𝐸 = 𝑚𝑔∆ℎ Joules Difference in potential energy is equal to
𝑝
the mass times gravity times the difference
in height
𝑝𝑜𝑤𝑒𝑟 = 𝐹𝑣 Watt or Power is equal to the force times velocity
Kg⋅m2⋅s−3
𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 %
𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑝𝑢𝑡
Momentum & Impulse
𝑝 = 𝑚𝑣 kg•m/s or N/s Momentum which is equal to mass times
velocity
𝐹=
∆𝑝 Newtons Force which is equal to the ratio of
∆𝑡
difference of momentum over the
difference of time
𝐸 =
𝑝² Joules Kinetic energy which is equal to the ratio of
𝑘 2𝑚
the square of momentum over twice the
mass
𝑖𝑚𝑝𝑢𝑙𝑠𝑒 = 𝐹∆𝑡 = ∆𝑝 Newton / Impulse which is equal to Force times the
second difference in time and is also equal to the
difference in momentum
Oscillations
𝑇=
1 seconds The period is equal to 1 over the frequency
𝑓
Travelling waves
𝑐 = 𝑓λ m/s The speed of a wave is equal to its
frequency times its wavelength
Wave characteristics
𝐼∝𝐴² W/m² Intensity is proportional to the square of
the area
𝐼∝𝑥⁻² W/m² Intensity is proportional to the inverse
square of displacment
𝐼 = 𝐼 0𝑐𝑜𝑠(θ)² W/m² Intensity of polarizer is equal to the initial
intensity times the square of cos of the
angle
Equation Unit Explanation
Uncertainties
If 𝑦 = 𝑎 ± 𝑏 Arbitrary → absolute uncertainty
Then: ∆𝑦 = ∆𝑎 + ∆𝑏
If 𝑦 =
𝑎𝑏 Arbitrary → fractional uncertainty
𝑐
∆𝑦 ∆𝑎 ∆𝑏 ∆𝑐
Then: 𝑦
= 𝑎
+ 𝑏
+ 𝑐
If 𝑦 = 𝑎^𝑛 Arbitrary → fractional uncertainty of which is equal
∆𝑦
Then 𝑦 = ||𝑛
∆𝑎 | to the fractional uncertainty of a^n
𝑎 | n = exponent of a (constant)
y:
a : measured value
Vectors & Scalars
𝐴 = 𝐴𝑠𝑖𝑛θ arbitrary Think of trigonometry → horizontal vector
ℎ
𝐴 = 𝐴𝑠𝑖𝑛θ arbitrary → vertical vector
𝑣
Motion
𝑣 = 𝑢 + 𝑎𝑡 metres/secon velocity
𝑣² = 𝑢² + 2𝑎𝑠 d
𝑠 = 𝑢𝑡 +
1
𝑎𝑡² metres displacement
2
(𝑣+𝑢)𝑡
𝑠= 2
Forces
𝐹 = 𝑚𝑎 Newtons Force exerted on object which is equal to
the mass times the acceleration of an
object
𝐹 ≤ µ 𝑠𝑅 Newtons Friction is equal or inferior to coefficient of
𝑓
friction times normal force for static object
𝐹 = µ 𝑅 Newtons Friction is equal to coefficient of friction
𝑓 𝑑
times normal force for dynamic object
Work, energy & power
𝑊 = 𝐹𝑠 𝐶𝑜𝑠θ Joules Work equal to the force times the
displacement times the cosine of the angle
of displacement
, 𝐸 =
1
𝑚𝑣² Joules Kinetic energy equal to half the mass of the
𝑘 2
object times the square of its velocity
𝐸 =
1
𝑘∆𝑥² Joules Potential energy equal to half the spring
𝑝 2
constant times the difference of x square
∆𝐸 = 𝑚𝑔∆ℎ Joules Difference in potential energy is equal to
𝑝
the mass times gravity times the difference
in height
𝑝𝑜𝑤𝑒𝑟 = 𝐹𝑣 Watt or Power is equal to the force times velocity
Kg⋅m2⋅s−3
𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 %
𝑡𝑜𝑡𝑎𝑙 𝑖𝑛𝑝𝑢𝑡
Momentum & Impulse
𝑝 = 𝑚𝑣 kg•m/s or N/s Momentum which is equal to mass times
velocity
𝐹=
∆𝑝 Newtons Force which is equal to the ratio of
∆𝑡
difference of momentum over the
difference of time
𝐸 =
𝑝² Joules Kinetic energy which is equal to the ratio of
𝑘 2𝑚
the square of momentum over twice the
mass
𝑖𝑚𝑝𝑢𝑙𝑠𝑒 = 𝐹∆𝑡 = ∆𝑝 Newton / Impulse which is equal to Force times the
second difference in time and is also equal to the
difference in momentum
Oscillations
𝑇=
1 seconds The period is equal to 1 over the frequency
𝑓
Travelling waves
𝑐 = 𝑓λ m/s The speed of a wave is equal to its
frequency times its wavelength
Wave characteristics
𝐼∝𝐴² W/m² Intensity is proportional to the square of
the area
𝐼∝𝑥⁻² W/m² Intensity is proportional to the inverse
square of displacment
𝐼 = 𝐼 0𝑐𝑜𝑠(θ)² W/m² Intensity of polarizer is equal to the initial
intensity times the square of cos of the
angle
