Quantities and Units in Mechanics

Introduction to Quantities and Units

Understand the role of quantities as physical, measurable properties that can be compared and calculated.
Recognise units as an established standard used for measuring a particular physical quantity.
Familiarise yourself with basic measurement units of fundamental quantities like time, mass, and length in the International System of Units (SI).

Appreciate the function of dimensional analysis in checking physical equations’ consistency and converting units.
Become accustomed to the seven base SI units from which all other SI units can be derived; these are ampere, kelvin, second, metre, kilogram, candela, and mole.
Understand the importance of universal measurement standards in providing consistency, reproducibility, and accuracy in calculations and experiments.

Comprehend the concept of derived units, which are formed by combining the base units in accordance with the algebraic relations of the quantities.
Remember important derived units such as newton, joule, watt, and pascal, which are used in mechanics.
Confidently perform unit calculations using conversion factors to switch between different systems of units or magnitude of units.

Become comfortable with the mechanics-specific units: newton for force, joule for work and energy, and watt for power.
Note that newton is a derived unit - equal to the force needed to accelerate a one-kilogram mass by one metre per second squared.
Recognise the joule as the work done by a force of one newton over a displacement of one metre.
Understand the watt as a unit of power, representing one joule per second.

Familiarise yourself with context-specific unit usage - g/cm³ for density, m/s for speed, or kg·m² for moment of inertia.
Understand how units can aid in problem-solving and interpretation - units in an equation should balance, which can be checked using dimensional analysis.
Regularly practice using quantities and units in mechanics problems to enhance understanding and fluency.
Utilise worked examples to consolidate knowledge and improve problem-solving abilities. Always revisit and re-solve problems independently to ensure thorough understanding.

Distinguish between the concepts of precision (how closely repeated measurements agree with each other) and accuracy (how close a measurement is to its true value).
Understand the sources and types of experimental errors and use appropriate techniques to reduce and account for errors in measurements.
Appreciate the importance of reporting measurements along with their uncertainties in order to portray the reliability of results.
Know how to calculate the absolute error, percentage error, and propagate error in mathematical operations.