Quantities and units in mechanics
Basic Principles
- Understand the concept of physical quantities; these are anything that can be measured (mass, length, time, etc.) in mechanics.
- Every physical quantity has a unit of measurement linked to it (kilograms, metres, seconds, etc.).
- Learn to identify scalar quantities (only magnitude) and vector quantities (both magnitude and direction).
Mechanic Quantities and their Units
- Mass (M): This is a scalar quantity. The unit of mass is the kilogram (kg).
- Length (L): This can be a scalar or vector quantity. The unit of length is the meter (m).
- Time (T): A scalar quantity. The unit of time is the second (s).
- Speed/ Velocity (V): Speed is a scalar quantity while Velocity is a vector quantity. Both have units of meter per second (m/s).
- Acceleration (a): Vector quantity. Unit is meter per second squared (m/s²)
- Force (F): Vector quantity. Unit is Newton (N) or kg.m/s².
- Momentum (p): Vector quantity. Unit is kg. m/s.
- Work done (W), Energy (E), and Power (P): Scalar quantities. Units are Joules (J) for work done and energy, and Watt (W) for power.
The Importance of Dimensions
- Understand the concept of dimensions, which are the powers to which the basic quantities must be raised to represent a derived quantity.
- Dimensions are always written in square brackets, e.g. [L] for length.
- Might be required to provide the dimensions for a physical quantity in questions.
Conversions
- Learn to convert different units, like km/h to m/s, kg to g, etc.
- Practice dimensional analysis, which is a method of checking the likely correctness of an equation by considering the dimensions of the quantities on each side of it.
Significant Figures
- Learn to present answers to an appropriate number of significant figures.
- Distinguish between the absolute error, fractional error, and percentage error in measurements.
Implications of Errors in Mechanics
- Understand the implications of errors in calculations, how quantities are affected by small changes, and how these changes propagate through calculations.
- Practice understanding the mechanics of real-world objects where small variations can have significant impacts.