Units and Measurements — Class 11 Maharashtra HSC Physics revision notes
A 7-page visual revision sheet for Units and Measurements, written for Class 11 Maharashtra HSC Physics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Units and Measurements in one look
seven units, honest digits, and how wrong you're allowed to be
The seven fundamental units
- Length: metre (m)
- Mass: kilogram (kg)
- Time: second (s)
- Temperature: kelvin (K)
- Electric current: ampere (A)
- Luminous intensity: candela (cd)
- Amount of substance: mole (mol)
A physical quantity
- a physical quantity = a number × a unit: without its unit the number means nothing
- change the unit and the number changes the other way: n_1u_1 = n_2u_2
Prefixes
- a prefix is a power of ten on the unit: shift the decimal point
The two supplementary units
- plane angle: radian (rad), dθ = ds/r, arc over radius
- solid angle: steradian (sr), dΩ = dA/r^2; a whole sphere subtends 4π sr
- both are ratios of like quantities, so both are dimensionless
Conventions for writing SI units
- full name starts small even for a person (newton, joule); the symbol is capital (N, J)
- no plural, no full stop: 20 N, never 20 Ns or 20 N.
- one ratio: m/s^2 or m s^-2, never m/s/s
- never mix a name with a symbol: J/kg K, not joule/kg K
- one prefix only: 10^-6 s is a microsecond, never 1 mms
- a space between multiplied units: ms is a millisecond, m s^-1 a speed
Page 1 of 7. The full sheet, all 7 pages, opens free in the app.
What this Units and Measurements sheet covers
- SI units
- The seven fundamental units
- Length
- Mass
- Time
- Temperature
- Electric current
- Luminous intensity
- Amount of substance
- A physical quantity
- Prefixes
- The two supplementary units
- Conventions for writing SI units
- Units for the very large and the very small
- 1 astronomical unit (AU)
- 1 light year
- 1 parsec (pc)
- 1 fermi (fm)
- 1 angstrom
- 1 atomic mass unit (u)
- How the metre, kilogram and second are fixed now
- measurement of length
- large distances
- Parallax: measuring what you cannot reach
- distance of a far object, basis b, parallax angle θ in radian
- diameter from its angular diameter α
- for a star, the basis is the Earth's orbit
- A sense of scale, order of magnitude
- dimensional analysis
- Dimensions of common quantities
- force
- work, energy
- power
- pressure, stress
- density
- momentum, impulse
- When all three powers are zero
- Principle of homogeneity
- Three jobs dimensional analysis does
- Where dimensional analysis fails
- Accuracy vs precision
- Accuracy
- Precision
- error analysis
- errors in measurement
- Systematic and random errors
- Systematic
- Random
- Errors, defined
- mean, the most probable value
- absolute error in one reading
- mean absolute error
- relative error; × 100\% for the percentage error
- Combining errors
- sum or difference, Z = A ± B
- product or quotient, Z = AB or A/B
- a power, Z = A^pB^q/C^r
- Products and powers
- Least count and vernier callipers
- 10 VSD = 9 MSD: 0.1 mm; 20 VSD = 19 MSD: 0.05 mm
- main scale, then the line that coincides
- Screw gauge
- one turn's pitch over the circular divisions
- pitch scale, then the index line
- Significant figures, counting rules
- Significant figures in calculations
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Physics chapter by chapter against your real exam dates and free hours, and when the plan reaches Units and Measurements the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.