What are the base and derived quantities of mechanics, and how do you distinguish scalars from vectors and model a real situation?
The SI base and derived units used in mechanics, the distinction between scalar and vector quantities, and the standard modelling assumptions such as particles, light strings and smooth surfaces.
A focused answer to the OCR A-Level Mathematics A mechanics quantities content, covering the SI base and derived units, the distinction between scalar and vector quantities, the standard modelling assumptions (particle, light, inextensible, smooth, rigid), and why these idealisations are made.
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What this dot point is asking
OCR wants you to use the SI base and derived units that appear in mechanics, distinguish scalar quantities (magnitude only) from vector quantities (magnitude and direction), and understand the standard modelling assumptions (particle, light, inextensible, smooth, rigid) and why they are made. This underpins every mechanics question, because a clear model and consistent units are the starting point for the equations.
The answer
SI units in mechanics
Mechanics is built on three base quantities and the derived quantities formed from them.
Keeping units consistent matters: convert everything to kilograms, metres and seconds before substituting, or the numbers will be wrong even when the method is right.
Scalars and vectors
A scalar has size only; a vector has size and direction. The distinction drives the mathematics: vectors must be resolved into components or combined head to tail, while scalars simply add.
Weight versus mass
Mass (a scalar, in kg) measures the amount of matter and does not change with location. Weight (a vector, in N) is the gravitational force on that mass: , directed downwards, with m s in this course.
Examples in context
Why model with idealisations
Real objects are complicated, so mechanics replaces them with idealised models that keep the essential physics and discard the awkward detail. Each assumption removes a specific complication.
The standard vocabulary
You should know the precise meaning of each modelling word, because questions test them directly. A light object has negligible mass (so its weight is ignored and a string's tension is uniform). An inextensible string does not stretch (so connected objects share one acceleration). A smooth surface has no friction; a rough surface does. A rigid body keeps its shape (used for rods and beams in moments problems).
Try this
Q1. A mass of g hangs from a string. Find its weight, taking m s. [2 marks]
- Cue. Convert to kg, then N.
Q2. Classify acceleration and distance as scalar or vector. [1 mark]
- Cue. Acceleration is a vector; distance is a scalar.
Exam-style practice questions
Practice questions written in the style of OCR exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
OCR 20194 marksState whether each of the following is a scalar or a vector: speed, velocity, distance, displacement, mass and weight. For one vector quantity, explain what extra information it carries compared with the corresponding scalar.Show worked answer →
Scalars (magnitude only): speed, distance, mass (B1 for a correct group). Vectors (magnitude and direction): velocity, displacement, weight (B1).
A correct full classification scores both marks; one slip drops one mark (A1, A1 awarded for accuracy).
Explanation: velocity carries a direction as well as a size, whereas speed is just the size; so a velocity of m s east differs from m s west, but both have speed m s (B1 for a clear contrast).
Markers reward the correct scalar/vector split and a clear statement that the vector adds direction to the scalar's magnitude.
OCR 20214 marksA box is pulled across a floor by a rope and modelled as a particle on a rough horizontal surface, with the rope light and inextensible. Explain what each of the modelling assumptions 'particle', 'light' and 'inextensible' means, and give one reason such assumptions are made.Show worked answer →
Particle: the box is treated as a point mass, so its size and shape are ignored and rotation does not occur (B1).
Light: the rope has negligible mass, so its weight is ignored and the tension is the same throughout (B1).
Inextensible: the rope does not stretch, so the box and the pulled end share the same speed and acceleration (B1).
Reason: these idealisations make the problem tractable, removing complications (deformation, rope mass, stretch) so the core physics can be modelled with simple equations (B1).
Markers reward a correct meaning for each of the three terms and a sensible justification for modelling.
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Sources & how we know this
- OCR A Level Mathematics A (H240) specification — OCR (2017)