# CIE AS & A Level Physics 9702: Topic 1: Physical quantities and units- Unit : 1.2 SI units Study Notes

 • Base quantities are the quantities on the basis of which other quantities are expressed. • The quantities that are expressed in terms of base quantities are called derived quantities

• SI Units – International System of Units

### Derived quantity & equations

• A derived quantity has an equation which links to other quantities.
• It enables us to express a derived unit in terms of base-unit equivalent.

Example: $\mathrm{F}=\mathrm{ma} ;$ Newton $=\mathrm{kg} \mathrm{m} \mathrm{s}{ }^{-2}$
$\mathrm{P}=\mathrm{F} / \mathrm{A} ; \quad \text { Pascal }=\mathrm{kg} \mathrm{m} \mathrm{s} \mathrm{m}^{-2} / \mathrm{m}^2=\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-2}$

### Some derived units

### SI Units

1. Equation: area $=$ length $\times$ width
In terms of base units: Units of area $=\mathrm{m} \times \mathrm{m}=\mathrm{m}^2$
2. Equation: volume $=$ length $\times$ width $\times$ height
In terms of base units: Units of volume $=\mathrm{m} \times \mathrm{m} \times \mathrm{m}=\mathrm{m}^3$
3. Equation: density $=$ mass $\div$ volume
In terms of base units: Units of density $=\mathrm{kg} \mathrm{m}^{-3}$

• Work out the derived quantities for:

1. Equation: $\quad$ speed $=\frac{\text { distance }}{\text { time }}$
In terms of base units: Units of speed $=\mathrm{ms}^{-1}$
2. Equation: $\quad$ acceleration $=\frac{\text { velocity }}{\text { time }}$
In terms of base units: Units of acceleration $=\mathrm{ms}^{-2}$
3. Equation: force $=$ mass $\times$ acceleration
In terms of base units: Units of force $=\mathrm{kg} \mathrm{ms}^{-2}$

• Work out the derived quantities for:

1. Equation: $\quad$ Pressure $=\frac{\text { Force }}{\text { Area }}$
In terms of base units: Units of pressure $=\mathrm{Kgm}^{-1} \mathrm{~s}^{-2}$
2. Equation: Work $=$ Force $\times$ Displacement
In terms of base units: Units of work $=\mathrm{Kgm}^2 \mathrm{~S}^{-2}$
3. Equation: Power $=\frac{\text { Workdone }}{\text { Time }}$
In terms of units: Units of power $=\quad \mathrm{Kgm}^2 \mathrm{~s}^{-3}$

### SI Units – Fill in…

### For you to know…

### Key Concept

1. A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit.
2. The physical quantities can be classified into base quantities and derived quantities.
3. There are seven base quantities: length, mass, time, current, temperature, amount of substance and luminous intensity.
4. The SI units for length, mass, time, temperature and amount of substance, electric current are metre, kilogram, second, kelvin, mole and ampere respectively.

### Homogeneity of an equation

• An equation is homogeneous if quantities on BOTH sides of the equation has the same unit.
•  E.g. $s=u t+1 / 2 a^2$
• LHS : unit of $s=m$
• RHS : unit of ut $=\mathbf{m s}^{-1} \mathrm{xS}_{\mathrm{x}}=\mathbf{m}$
•  Unit on LHS = unit on RHS
• Hence equation is homogeneous

### Non-homogeneous

• $\mathrm{P}=\rho g h^2$
•  LHS ; unit of $\mathrm{P}=\mathrm{Nm}^{-2}=\mathrm{kgm}^{-1} \mathrm{~s}^{-2}$
•  RHS : unit of $\rho \mathrm{gh}^2=\mathrm{kgm}^{-3}\left(\mathrm{~ms}^{-2}\right)\left(\mathrm{m}^2\right)=\mathrm{kgs}^{-2}$
•  Unit on LHS $\neq$ unit on RHS
• Hence equation is not homogeneous

### Homogeneity of an equation

•  Note: numbers has no unit
•  some constants have no unit.
• e.g. $\pi$
• A homogeneous eqn may not be physically correct but a physically correct eqn is definitely homogeneous
• E.g. $s=2 u t+a t^2$ (homogenous but not correct)
•  $\quad \mathbf{F}=\mathbf{m a} \quad$ (homogeneous and correct)

### Magnitude

• Prefix : magnitudes of physical quantity range from very large to very small.
•  E.g. mass of sun is $10^{30} \mathrm{~kg}$ and mass of electron is $10^{-31} \mathbf{k g}$.
• Hence, prefix is used to describe these magnitudes.

### Significant number

•  Magnitudes of physical quantities are often quoted in terms of significant number.
•  Can you tell how many sig. fig. in these numbers?
•  103, 100.0, 0.030, 0.4004, 200
•  If you multiply 2.3 and 1.45, how many sf should you quote?
•  3.19, 3.335, 3.48
•  3.312, 3.335, $3 \cdot 358$
Scroll to Top