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

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

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.

Example 3

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

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

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Force $$1$$ is air resistance.

Force $$2$$ is weight.