Quantities and units in mechanics — Edexcel A-Level Mathematics
Test yourself on Quantities and units in mechanics with PEARSON EDEXCEL A-Level practice questions.
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Quantities and units in mechanics explained
Mechanics begins with three fundamental S.I.
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quantities: length measured in metres (m), time in seconds (s) and mass in kilograms (kg). Derived quantities are formed by combining these. Velocity is displacement per unit time, with unit m s⁻¹; acceleration is velocity change per unit time, with unit m s⁻². Force is mass times acceleration, so its unit is kg m s⁻², named the newton (N). Weight is the force of gravity on a mass, W = mg, also measured in newtons, where g is about 9.8 m s⁻² near the Earth's surface. Moment is the turning effect of a force about a point, defined as force times perpendicular distance, with unit N m. Checking that every term in an equation has consistent units is a powerful way to detect errors.
Your focus
- State the fundamental S.I. quantities and their units.
- Derive and use units for velocity, acceleration, force, weight and moment.
- Distinguish between mass and weight and between force and moment in calculations.
Quantities and units in mechanics exam tips
Marking Points
- State the fundamental S.I. quantities as length, time and mass with units m, s and kg respectively.
- Derive the unit of velocity as m s⁻¹ and acceleration as m s⁻² from their definitions as rates of change.
- Show that force has unit kg m s⁻², equivalent to the newton, from F = ma.
- Distinguish weight as a force, W = mg, measured in newtons, from mass measured in kilograms.
- Define moment as force multiplied by perpendicular distance and give its unit as N m.
Examiner Tips
- 💡Carry units through every line of working so inconsistencies are visible immediately.
- 💡Convert grams to kilograms and centimetres to metres before substituting into formulae.
- 💡When asked to distinguish quantities, name the quantity, its symbol, its unit and whether it is scalar or vector.
Common Mistakes
- Treating weight and mass as the same quantity; the correction is that mass is in kg while weight is a force in N given by W = mg.
- Writing the unit of force as kg m s⁻¹; the corrected unit is kg m s⁻², since acceleration is m s⁻².
- Using the distance along the line of action rather than the perpendicular distance when computing a moment; the corrected method uses the perpendicular distance from the pivot.