GCE O-Level Physics Notes

Chapter 1: Measurements

Content:

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Learning Outcomes:

Students should be able to

Show understanding that all physical quantities consist of a numerical magnitude and a unit.
Recall the following base quantities and their units:
- mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
Use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units:
- nano (n), micro (µ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G)
Show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth.
State what is meant by scalar and vector quantities and give common examples of each.
Add two vectors to determine a resultant by a graphical method.
Describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary.
Describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments.

SI Units:

There are 7 base units:

Meters (m), Kilogram (kg), Second (s), Ampere (A), Kelvin (K), Mole (Mol), and Candela (cd)

Each unit corresponds with one of the 7 physical quantities:

Length, Mass, Time, Current, Temperature, Amount of Substance, and Light Intensity.

Base Quantity	Symbol	SI Units	Base Unit / Symbol for Units
Length	𝓛	metre	m
Mass	m	kilogram	kg
Time	t	second	s
Current	I	ampere	A
Temperature	T	Kelvin	K
Luminous Intensity	L	candela	cd
Amount of Substance	n	mole	mol

Derived Units:

Any unit that is defined in terms of the base units. They are expressed as products or quotients of base units.

Derived Quantities	Equation	Derived Units
Volume (V)	V=L^3	m^3
Area (A)	A=L^2,L ∶ Length	m^2
Acceleration (a)	a=Δv/Δt, Δ : "change in"	m s^-2
Velocity (v)	v=L/t, t : time	m s^-1
Density (ρ)	ρ=m/V, m : mass	kg m^-3
Force (N)	F=ma, m : mass, a : acceleration	kg m/s^2
Momentum (p)	p=mv	kg m s^-1
Work Done	W=fd, f : force, d : distance	(kg m^2)/s^2
Voltage	V=w/q, w : work done, c : charge, c=It, I : current; V=w/(It)	(kg m s^-2)/(s^3 *A)

Homogenous Equations:

An equation is said to be homogenous or dimensionally consistent if every term on both sides of the equation has the same base units.

A homogenous equation may not be true or correct.

Systematic Errors:

When all the readings of an experiment are consistently larger or smaller than the true value by a fixed amount.

Random Errors:

When the readings of an experiment are randomly scattered about a mean value.

Accuracy:

The degree of closeness of the experimental values to the true value.

Measured by comparing the average of multiple experimental readings to the true value.

Precision:

The degree of agreement between repeated measurements of the same quantity.

Scalar Quantity:

Physical quantities with magnitude only.

Vector Quantity:

Physical quantities with both magnitude and direction.

Prefix:

Signifies powers of 10, written before numbers to make them easier to read and understand.

Uncertainty:

Uncertainty is the range of possible values within which the true value of the measurement lies.

1.	Addition	R=aX + bY	Absolute Uncertainty is ΔR=\|a\|ΔX+\|b\|ΔY
2.	Subtraction	R = aX - bY	Absolute Uncertainty is ΔR=\|a\|ΔX+\|b\|ΔY
3.	Product	R = aX * bY	Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y
4.	Division	R = aX/Y	Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y
5.	Product with Powers	R = (aX^m) * (Y^n)	Fractional Uncertainty is ΔR/R = \|m\|(ΔX/X) + \|n\|(ΔY/Y)
6.	Quotient with Powers	R = (aX^m)/(Y^n)	Fractional Uncertainty is ΔR/R = \|m\|(ΔX/X) + \|n\|(ΔY/Y)
7.	Special Functions	Any functions such as sine, cosine, etc.	Uncertainty of R is (Rmax + Rmin)/2, R = (Rmax + Rmin)/2 ± (Rmax - Rmin)/2