## Measurement Of Time - From Sundial, Hourglass To Atomic Clock

Time is an extremely perplexing concept. The Measurement of Time is incredibly accurate but we don’t have a definition for it. We can feel time but we cannot explain it. Time is a measure in which events can be organised and ordered from the past to the present and the future.

## Significant Figures: Rules For Arithmetic Operations

Arithmetic is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises of operations such as Addition, Subtraction, Multiplication and Division.

## Significant Figures: Errors In Measurements

The significant figures of numbers are digits convey the meaning that contributes to its measurement resolution. The number 13.2 is comprised of three significant digits. Non-zero digits are always significant. 3.14159 has 6 significant digits (all the numbers give you useful information). Thus, 67 has 2 significant digits, and 67.3 has three significant digits.

## Dimensional Analysis and its Application

While using addition and subtraction for two or more physical quantities, we notice that only those quantities can be added or subtracted that have similar dimension. On the other hand, in the case of multiplication and division, when two quantities are multiplied, along with their magnitudes, the dimensions are also treated accordingly, in order to find the dimension of the product.

## Dimensions of Physical Quantities and Dimensional Analysis in Physics

### Dimensions of Physical Quantities

In physics and engineering, physical quantities are composed of a set of numbers with fundamental quantities. Every other physical unit of measurement or quantity can be mentioned in terms of the fundamental quantities. In other words, dimension is an expression of the character of a derived quantity about fundamental quantities, without regard for its numerical value.

## Errors In Measurement

Any measurement that you make is just an approximation, 100% accuracy is not possible. If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called a **variation** in the measurements.

## Accuracy And Precision - The Art Of Measurement

Why do we need measurement? Measurement is the foundation for all experimental science and technology. Science is the study of nature and we need to use what we see in nature in our calculations. Today we know that the acceleration due to gravity is 9.8 m/s^{2} but would we be able to comprehend that if we had no means of measurement.

## Measurement of Mass: Mass and Weight

Mass is a basic characteristic property of matter. It exists self-sufficiently and is independent of all other parameters such as the temperature, pressure, and the location of the object in space. Atomic mass is the mass of an atom expressed in atomic mass units. Matter has mass and occupies space.

## Measurement Of Length: Triangulation And Parallax Method

### Measurement by Triangulation

Let’s try to understand what exactly do we mean by the parallax method? How can triangulation help us measure the distances of faraway stars. The parallax method uses the fact that a triangle can be described completely with only three elements. This method of finding the values of the triangle to yield the location of an object is termed as **Triangulation**.

## The SI Units

The **International System of Units** or SI Units in short is a set of units using a metric system. A system is metric if units are defined in terms of powers of ten. For example, \(1 kilogram\) = \(10^3 grams\). However, since the SI is the most popular system of metric units, it is generally simply referred to as the **metric system**.

## Laws Of Physics

By nature, laws of physics are **stated facts** which have been deduced and derived based on empirical observations. Simply put, the world around us works in a certain way, and physical laws are a way of classifying that "working".

## Forces: Fundamental Forces In Nature

There are **four universal or fundamental forces in nature**. Without these forces, all matter in the world will fall apart. Force as such is any pull or push that causes an object to alter its physical state (in terms of motion or deformity). Newton defined a force as anything that causes an object of mass ‘m’ to move with an acceleration ‘a’.

## Technology And Society, Physics

For the improvement and advancement of society, we have grown to depend on the enhancement of technology available to us. For the enhancement of technology, we have to depend on the sciences, particularly the physics of it all. Unless the idea hatching in an inventor’s brain doesn’t conform to the laws of nature, its existence isn’t feasible.

## The Scope And Excitement Of Physics

### Scope of Physics

The scope of classical Physics deals with the following branches in Physics

- Classical Mechanics
- Thermodynamics
- Electromagnetism
- Optics

## Physics Definition - What Is Physics

It is simply the **study of the world around us**. For example: when a ball is thrown up in the air comes back to the ground the study of motion of this ball is physics, the study of elasticity of spring is physics, the study of twinkling of stars is physics.

## Algebra of Events

Number of favorable outcomes to the total number of outcomes is defined as the **probability of occurrence** of any event.

## Events In Probability

The entire possible set of outcomes of a random experiment is **sample space** of that experiment. The likelihood of occurrence of an event is known as **probability**. The probability of occurrence of any event lies between 0 and 1.

## Bernoulli Trials and Binomial Distribution

Many random experiments that we carry have only two outcomes that are either failure or success. For example, a product can be defective or non-defective, etc. These types of **independent trials which have only two possible outcomes are known as Bernoulli trials**.

## Mean And Variance Of Random Variable

Probability distribution of a random variable is defined as a description accounting the values of the random variable along with the corresponding probabilities. In many cases we express the feature of random variable with the help of a single value computed from its probability distribution. These values can either be **mean or median or mode**.

## Probability Distribution of Random Variable

In most of the random experiments that we perform, we are not only interested in the particular outcome of the experiment but in some number associated with that outcome. For example: when we roll a pair of dice, we may be interested in the sum of numbers that appears on the dice. In such experiments, a single real number is assigned to each outcome of the experiment.

## Conditional Probability: Bayes' Theorem

Bayes’ theorem describes the probability of occurrence of an event related to any condition. For example, if you have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls, where each bag contains three different color balls viz. red, blue, black. Such case where probability of occurrence of an event is calculated depending on other conditions is known as **conditional probability**.

## Total Probability Theorem

For two events A and B associated with a sample space S, the sample space can be divided into a set {\(A\cap B′, A\cap B, A′ \cap B, A′ \cap B′\)}. This set is said to be **mutually disjoint** or pairwise disjoint because any pair of sets in it is disjoint. Elements of this set are better known as a partition of sample space. This can be represented by the Venn diagram. In cases where the probability of occurrence of one event depends on the occurrence of other events, we use total probability theorem.

## Independent Events And Probability

If probability of occurrence of an event A is not affected by occurrence of another event B, then A and B are said to be **independent events**. Consider an example of rolling a die. If A is the event ‘the number appearing is odd’ and B be the event ‘the number appearing is a multiple of 3’.

## Multiplication Rule of Probability

For two events A and B associated with a sample space \(S\), the set \(A∩B\) denotes the events in which both event \(A\) and event \(B\) have occurred. Hence, \((A∩B)\) denotes the **simultaneous occurrence of the events** \(A\) and \(B\). The event A∩B can be written as \(AB\).

## Conditional Probability And Its Examples

Imagine a student who takes leave from school twice a week excluding Sunday. If it is known that he will be absent from school on Tuesday then what are the chances that he will also take a leave on Saturday in the same week? It is observed that in problems where the occurrence of one event affects the happening of the following event. These cases of probability are known as **conditional probability**.

## Axiomatic Probability

In normal approach to probability, we consider random experiments, sample space and other events that are associated with the different experiments. In our day to day life, we are more familiar with the word ‘chance’ as compared to the word ‘probability’. Since, Mathematics is all about quantifying things, the theory of probability basically quantifies these chances of occurrence or non-occurrence of the events.

## Probability

Probability is the** measure of the likelihood of an event to occur**. Many events cannot be predicted with total certainty. We can predict only the chance of event to occur, how likely they are to happen, using probability. Probability can range in between 0 to 1, where 0 probability means the event to be an impossible one and probability 1 indicates the certain event.

## Theoretical Probability

Every one of us would have encountered multiple situations in life where we had to take a chance or risk. Depending on the situation, it can be predicted up to a certain extent if a particular event is going to take place or not. This **chance of occurrence of a particular event** is what we study in probability.

## Empirical And Theoretical Probability

Before talking about empirical and theoretical probability, we first recall what probability is. We come across a number of situations every day where we need to predict the outcome of an event before the event has taken place. We often use the statements like ‘it might rain today’ or ‘chances are that I will reach on time’, etc. Thus, there are many events whose outcome cannot be foreseen; they are decided by **chance**.

## Empirical Probability

If I were to ask you which cricket team had a greater chance of beating India - Australia or South Africa, what would be your answer? There is no way for you to precisely determine and compare the chances of the two events happening. The concept of chance and possibility of an event intrigued the mathematicians of the age.

## Experimental Probability

You and your 3 friends are playing a board game. It’s your turn to roll the die and to win the game you need a 5 on the dice. Now, is it possible that upon rolling the die you will get an exact 5? No, it is a matter of chance. We face multiple situations in real life where we have to take a **chance or risk**.

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