1. Physical quantities, Units and Measurement
CIE O Level Physics (5054) Syllabus Notes
Physics involves the study of various physical quantities.
A
physical quantity is a physical property that can be quantified (it can be measured and expressed with numbers).
Examples of physical quantities: mass, length, time, temperature, electric current and many others.
A physical quantity is the product of a numerical value (magnitude) and a unit of measurement.
Physical Quantity = Numerical value x Unit of measurement
For example in a force of 3N, 3 is the numerical value and N, Newton is the unit of measurement.
SI Units: SI units is the international system of units. It is used by scientist all around the world to avoid confusion. It is consist of base physical quantities and their corresponding base units. These are:
All other physical quantities in physics are derived from the base physical quantities and are hence known as derived physical quantities and derived units.
Prefixes:
Prefixes are powers of ten.
These are used to avoid very large and very small numerical values.
Some commonly used prefixes are:
* From here, you only need know 10^-12 to 10^!2
Examples:
One milliampere (mA) is 1 x 10^-3
3MJ (MegaJoule) = 3 x 10^6
* Note: The symbol of milli is small letter (m) and mega is capital letter (M).
Don't get confused! :)
Scalars and Vectors:
All physical quantities can be categorized into two terms:
- Scalar quantities
- Vector quantities
Scalar quantities are physical are physical quantities that require only
magnitude to be defined completely.
Vector quantities are physical quantities that require both
magnitude and
direction to be defined completely.
Examples of scalar quantities/scalars: length, mass, time, speed, distance
Examples of vector quantities/vectors: displacement, velocity, acceleration, force
Explanation:
As you can see above, none of the scalar quantities require a specified direction when you talk about them. For example, when we talk about mass, we usually say, 2kgs, a 100gs, etc. However if talk about force and I say that I push a book that is kept on a table towards the right, it wouldn't get shifted to the left. It would only get shifted to the right. So the direction is important here!
In the same way, all other vectors require direction to defined and understood.
When you'll read the definitions of the other vector quantities mentioned above, you'll notice that most of them would emphasize their definition with the word "direction".
The perfect example of this is available in the second chapter where you have to distinguish between distance and displacement.
Solving the resultant of vectors geometrically:
Scalar quantities are calculated arithmetically while vector quantities are calculated geometrically.
A vector is represented by a straight line with an arrow. The length of the arrow represents the magnitude (unless stated otherwise in the question or a scale is given) and the arrow indicates the direction.
The resultant of two vectors is represented by the
resultant vector.
Vector Resultant vector
Rule 1:
If two vectors are acting in the
same direction, the resultant vector is the
sum of the two vectors.
If two vectors are acting in the
opposite direction, the resultant vector is the
difference between the two vectors.
When both the forces are acting in the same direction, the resultant force, R, is the sum of the two forces. This is because both the forces are acting in the same direction.
When both the forces are acting in opposite directions, R, is the difference between the two forces. The direction of R is in the direction of larger vector (in this case the vector is force).
Rule 2:
Triangle Rule
Vector triangles can be drawn using vector equations and vice versa.
* The following are the equations of the vector triangles. When two vectors are in the same direction, their signs(+/-) are same. If a vector is in the opposite direction, their sign is also opposite.
Q. Draw the vector triangle for the following equation:
a+b = c
If a + b = c
then a + b - c = 0
therefore,
Rule 3:
Parallelogram Rule:
If the length of two adjacent sides of a parallelogram represents two vectors. The diagonal of the parallelogram represents the resultant vector.
Rules:
1. Set a suitable scale. For this, I have taken 1N = 1cm
2. First draw one of the force. I have drawn a 3cm line
horizontally first and labelled it 3N.
3. Then with a protractor I measured out 60° from the left-end of the line and I marked the point.
4. Then at the point I drew a 5cm line and labelled it 5N.
5. The diagram now consists of two adjacent lines.
6. Now draw an exactly parallel 3cm dotted line from the top of 5N force. Now join the remaining two points with dotted lines to form a a parallelogram This line should be parallel to the 5cm line.
7. Draw the diagonal of the parallelogram.
8. Measure the length of the diagonal. I got 7cm and because my scale was 1cm = 1N, the resultant force, R = 7N.
* In many of these questions, you have to select the scale unless specified in the question. So if they give you forces such as 50N or 60N, taking taking the scale as 1N = 1cm/2cm wouldn't be suitable as the question paper wouldn't be that long! A suitable scale would be 1cm = 10N.
* The best way to master these type of questions is by practicing. So practice as many as you can from your textbook and also from the question paper.
* These are two questions relevant for this topic. Try solving these.
O/N 2001, Q-1, PAPER - 2 (
link) (
GOOD QUESTION!)
O/N 2008, Q-1, PAPER - 2 (
link)
The mark schemes are given in the links however if you still have any confusion ask me in the comments section below, I will try to answer as soon as I can.
Measuring length:
Length can be measured using various equipment.
Some of these are:
* Precision is the smallest possible value that can be read by an equipment.
How to measure using vernier caliper:
1. Read the main scale reading just before the zero mark on the vernier scale.
2. Read the vernier scale reading that coincides with the main scale reading. If more than one value coincides, take the lowest one.
3. Add the main scale reading to the vernier scale reading making sure that both are in same units.
How to measure using micrometer screw gauge:
1. Read the main scale reading at the edge of the circular scale. (the value may sometimes be in decimals, it should be taken care of when calculating).
2. The circular scale has 50 divisions, each of which is equal to 0.01mm. Take the circular scale reading opposite the datum line of the main scale.
3. Then multiply:
circular scale value x 0.01
4. Add the main scale reading to the circular scale reading, making sure both are in same units.
Measuring Time:
Time can be measured using analogue and digital stopwatches.
The precision of an analogue stopwatch is 1s and the precision of a digital stopwatch is 0.01s.
When measuring time using watches, the reading has to be taken manually and this involves human errors. This can be reduced by taking several readings and calculating the average.
