Quantities and units in mechanics

In a nutshell

The common quantities and units are given by the International System of Units (abbreviated SI). There are both base units and derived units.

Base SI Units

quantity	unit	symbol
$Mass$	$Kilogram$	$kg$
$Length/displacement$	$Metre$	$m$
$Time$	$Seconds$	$s$

Example 1

Write the following quantities in SI units:

a: $9\ km$

b: $2\ minutes$

c: $2300\ g$

a: The SI unit for length is $m$ . $1\ km=1000\ m$ , therefore $9\ km$ in SI units is:

$\underline{9000\ m}$

b: The SI unit for time is $seconds$ . $1\ minute = 60\ s$ , therefore $2\ minutes$ in SI units is:

$\underline{120\ s}$ 

c: The SI unit for mass is $kg$ . $1000\ g=1\ kg$ , therefore $2300\ g$ is:

$\underline{2.3\ kg}$ 

Derived units

quantity	unit	symbol
$Speed/velocity$	$Metres\ per\ second$	$ms^{-1}$
$Acceleration$	$Metres\ per\ second\ squared$	$ms^{-2}$
$Weight/force$	$Newtons$	$N\ or\ kgms^{-2}$

Example 2

Write $30kmh^{-1}$ in SI units:

The SI unit for distance is $m$ , therefore convert to $m\cdot h^{-1}$ by mutliplying by $1000$ :

$30\ km\cdot h^{-1}=30000\ m\cdot h^{-1}$

The SI unit for time is $s$ , therefore convert to $m\cdot s^{-1}$ by dividing by $3600$ :

$30000\ m\cdot h^{-1}=\underline{8.33\ m\cdot s^{-1}}$ 

Note: Kilograms do not measure weight, as many believe. Weight is a force which is measured in Newtons, and kilograms is used to measure mass. Weight is equal to the mass of an object multiplied by the acceleration of the object.

Force diagrams

There are a number of forces in mechanics, which will sometimes be labelled on diagrams, which act on objects in different directions.

quantity	Direction of force
Weight	Acts vertically downwards.
Normal reaction	Acts perpendicular to a surface when an object is in contact with the surface, in the opposite direction to the force applied to the surface by the object.
Friction	Acts in the opposite direction to the motion between two surfaces when one of them is rough.
Tension	When an object is being pulled along by a string, the force acting on the object is the tension in the string.
Thrust/compression	When an object is being pushed, the force acting on the object is called the thrust or compression.
Buoyancy	Acts upwards on objects to allow them to float when submerged in a liquid.
Air resistance	Acts in the opposite direction to motion.

Example 3

A fox is skydiving, as shown in the diagram. Identify the forces shown in the diagram.

Maths; Modelling in mechanics; KS5 Year 12; Quantities and units in mechanics

The forces shown in the diagram are labelled as $1$ and $2$ .

Force $1$ is air resistance.

Force $2$ is weight.