O LEVEL PHYSICS - KINEMATICS

Kinematics is a branch of Mechanics that is concerned with pure motion and is not concerned with the forces involving those motion. 

Distance (in terms of kinematics) is length covered by a moving object.
Displacement is the linear distance between two points.
Displacement is the linear distance traveled by an object from the starting point to the endpoint.
Linear distance means distance in a straight line.
The  SI units of both Distance and Displacement is in meters(m).
Distance is a scalar quantity.
Displacement is a vector quantity.

Let's look at this concept with an example.

Example 1:

Suppose a car travels from A to B and then from B to C (see diagram). What is the car's total distance and displacement?  

Answer: The car's total distance is the length that it moved. That is,
distance = 15 + 7 = 22m

And it's displacement is

displacement = 10m

Because this is the linear distance covered between the starting and the endpoint.



The car now further travels from C to A. What is now the car's total distance and displacement starting from A and traveling back to A?

Answer: Now the total distance will be,
distance = 22 + 20 = 40m

And the total displacement will be
displacement = 0m

Because the starting and endpoints are the same and there is zero meters of linear distance in between them.  






Now moving on to speed and velocity.

Speed is rate of change of distance. It is measured in meters per second (m/s). It is a scalar quantity.

speed = distance traveled / time taken

Velocity is the rate of change of displacement. It is also measured in meters per second (m/s). It is a vector quantity.

velocity = displacement / time taken  




You would find plenty of examples on speed/velocity calculations on your book. Therefore I am not adding another one here. Next we are going to look at Acceleration.

In the simplest of terms...


Acceleration is the rate of change of velocity. It is measured in meters per second square (m/s^2). 
It is vector quantity.   

acceleration = change in velocity / time taken
 
But the question still remains of what acceleration actually is or what is happens during acceleration.
So if we now look at a deeper definition...

Whenever there is a change in velocity, there is an acceleration. If the velocity is not changing then there is zero or no acceleration. But another thing to note is that velocity is a vector quantity so if the direction of an object changes, then it's velocity changes. Hence it's acceleration changes.
So, either change in magnitude or change in direction, both results in an acceleration. (This is an important point to note as this often comes as a conceptual question in CIE O Level Exams). 

There are two types of acceleration:

•  uniform acceleration
•  non-uniform acceleration  

Uniform acceleration
Uniform acceleration is when the rate of change of velocity remains constant.
Another name for uniform acceleration is constant acceleration. Constant acceleration means that the acceleration does not change but remains constant. It does not increase or decrease with time. 

Number - Mathematics D

Number
Cambridge O Level Mathematics D (4024)


This chapter would be quite long and might get boring at times as you might know most of these things. I would rather suggest you to go thoroughly through the number system and give the rest of  the chapter a quick read and update your what you've learned if you find anything unfamiliar.





Number systems:

Definitions of different types of numbers we use:

• Natural numbers: Natural numbers are counting numbers. Natural number include whole numbers only, however, it may or may not include 0 (zero). Natural numbers only include positive numbers.  E.g. {1, 2, 3, 4, 5,...}.
• Whole numbers: All non-fractional numbers are called whole numbers. It includes zero. E.g. { 0, 1, 2, 3, 4,...}. Any number like 0, 7, 212, 1023 are all whole numbers.
• Integers: Integers include all negative and positive non-fractional numbers (or whole numbers) and 0 (zero). E.g. {...-3, -2, -1, 0, 1, 2, 3,...}
• Rational numbers: Rational numbers are all numbers that can be expressed as a ratio or a fraction. This would be possible if both the numerator and denominator are whole numbers or more specifically integers. E.g. { 9.0, 8/1, 2/3, 0.55555} are examples of rational numbers. NOTE: If you put 2/3 in a calculator, you would get the number 0.66666666 and it would go on forever. These are also rational numbers and are expressed using a recurring decimal. A recurring decimal is a decimal number that has digits that repeat forever. 
• Irrational numbers: An irrational number is a number that cannot be expressed as a fraction. This is because in these numbers, there is not a finite number of numbers when written as a decimal. Instead, the numbers go on forever without repeating. Hence, these numbers can't either be expressed using a recurring decimal. E.g. { √2 = (1.41421356…), π = (3.14159265…)}
• Real numbers: A real number is any quantity on the number line. It includes all of the types of numbers mentioned above. E.g. {0, 1, 2, 2.5, 2/3, √2, π}. (√(−6), negative root of something is NOT a real number).
• Imaginary number: An imaginary number is a number which is not a real number. E.g. Negative root of something (√(−6)).

For the symbols of these numbers, refer to your math D syllabus, page#22.

O LEVEL PHYSICS CHAPTER 1

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.