# Jamb physics tutorial S02

by Philip Obhenimen · Published · Updated

**INTRODUCTION**

Welcome to another series of this **Jamb physics tutorial**. I hope you enjoyed the first series which was on **MEASUREMENT AND UNITS**. You can * click here* if you have not seen the first series. We will continue the series by dealing thoroughly with

**SCALARS AND VECTORS**. This

**jamb physics tutorial**will be very helpful as it will expose you to all possible formats questions can be set on

**SCALARS and VECTORS.**

Grab your writing material (Biro and jotter). Also, make sure you get a glass of chilled fruit drink or water to refresh yourself as we start up with this **Jamb physics tutorial** series on **Scalars and vector. **

In this **Jamb Physics Tutorial** **S02** series two we will achieve the following objectives:

- Why
**Scalars and Vectors** **Scalar**quantities- How to know if a physical quantity is a
**Scalar** - Examples of
**scalar quantities**and their**S.I unit** **Vector**quantities- How to know if a physical quantity is a
**vector** - Examples of
**vector quantities**and their**S.I unit** **Distance**and**Displacement**- The
**concept of Distance** - The
**concept of Displacement** - Difference between
**Distance**and**Displacemen**t using image **Mass**and**Weight**- Reason why
**weight**can**vary**from place to place

For those of you, that feel you are done this topic, you can jump right ahead to take the quiz which is at the end of the article by clicking the button below.

Mind you if you fail any question I recommend you come back to read this enriched write-up

**SCALAR QUANTITY**

**Scalar quantities** are physical quantities that have **magnitude but no direction**. This is the popular definition of scalar quantities.

In other words, a quantity is termed “Scalar” if the size of the quantity(magnitude), that is, how big or small the quantity is can give us sufficient information about that quantity.

**How to know if a physical quantity is a scalar**

**Scalar quantities** have certain characteristics that will help you to differentiate them from vectors. The characteristics are listed below.

**Scalar quantities**have only one characteristic which is**magnitude**.**Scalar quantities**can only explain**one-dimensional quantitie**s**Scalar quantities**change only when there is a**change in their magnitude**.**Scalar quantities**follow the rules of algebra, that is,**algebraic addition**,**algebraic subtraction, algebraic multiplication,**and**algebraic division**.**Comparing scalar quantities**involves comparing their**magnitude only**.

Let’s use mass as a scalar quantity to validate the characteristics we listed above;

When an engineer, physicist or a layman hear the word mass of a body he/she is interested in how big or how small that body is. This helps to validate the fact that mass is a one-dimensional quantity.

**SCALAR QUANTITIES AND THEIR UNITS**

**Mass**measured in**kg****Time**measured in**seconds (s)****Temperature**measured in**kelvin(K)****Area**measured in**m^{2}****Volume**measured in**m^{3}****Density**measured in**kg/m^{3}****Pressure,Stress,Young’s modulus**all measured in**N/m^{2}[/latex**]**Distance**measured in**m****Speed**measured in**m/s****Energy**measured in**joule (J)****Work**measured in**joule (J)****Power**measured in**watt (W)****Heat capacity**measured in**Joule/kelvin (J/K)**- Specific heat capacity measured in
**(J/kgk)** **Current**measured in**Ampere(A)****Magnetic flux**measured in**weber (wb)****Capacitance**measured in**farad (F)****Quantity of charge**measured in**coulomb(C)****Inductance**measured in**Henry(H)****Voltage**measured in**volt(V)****Electrical resistance**measured in**ohms(Ω)****Electric potential**measured in**volt (V)****Gravitational potential**measured in**(J/kg)**

Do you find it hard to concentrate while reading ** click here** to see the steps you can take to discipline yourself to study well.

**VECTOR QUANTITY**

**Vector quantities** are physical quantities that have **magnitude and direction**. This is a very popular and valid definition of vector quantities.

In other words, a quantity is termed ‘vector’ if we need to **specify both its magnitude (the size of the quantity) and direction** to completely define the quantity.

**How to know if a physical quantity is a vector**

**Vector quantity** has certain characteristics that will help you differentiate them from scalars. The characteristics are listed below:

**Vector quantities**have two characteristics which are**magnitude and direction****Vector quantities**can be used to explain**multi-dimensional quantities****Vector quantities**changes with a**change in**either**magnitude or direction or both****Vector quantities**follow the vector rules of algebra which is the**triangle law of addition or the parallelogram law****Comparing vector quantities**involves comparing them in**magnitude and direction**

**VECTOR QUANTITIES AND THEIR UNITS**

**Displacement**measured in**metre(m)****Velocity**measured in**metre per second (m/s)****Acceleration**measured in**metre per second squared ms^{-2}****Force**measured in**Newton(N)****Torque**measured in**Newton metre (N.m)****Moment**measured in**Newton metre (N.m)****Momentum**measured in**Kilogram metre per second(Kg.m/s)****Impulse**measured in**Newton second (N.s)****Electric field intensity**measured in**newton per coulomb (N/C)****Weight**measured in**Newton(N)****Magnetic field**measured in**weber per metre squared wb/m^{2} or Teslas(T)****Angular momentum**measured in**kg.m^{2}s^{-1}**

**Distance and Displacement**

The fact that **distanc**e is a **scalar quantity** while **displacement** is a **vector quantity** is not new to us.

Lets us take a deeper look into the concept of distance and displacement.

**The Concept of Distance**

Distance is the total length of the path a body moves without considering direction. A more practical example, when you stand up from your current position and probably visit your friend, the distance you have covered is the length of the path you took from your house to your friends’ place.

Also, please note that distance can neither be negative nor zero, that is, distance always has a positive value. If a person walked from his current position to a new position and the back to his former position, the distance he covered in the length of the path he took from his initial position to a new position plus the distance from the new position to his former position.

##### The concept of displacement

Displacement is a vector quantity, that is, it has both magnitude and direction.

Displacement is the distance between a point from a particular reference point. Most times, the reference point is taking as the starting point of motion of a body.

For example, if a boy goes from his house to his friends’ place, his displacement from his house(starting point) is the distance of the straight line joining his house and his friends’ house.

Moreover, if the boy travels back to his house then his new displacement will be zero (taking his house as the reference point)

**USING IMAGES TO DIFFERENTIATE DISTANCE AND DISPLACEMENT**

Considering the picture above, the guy moves from **start** to **end** following the **green path**.

Therefore, the **distance** he covers will be the **total length** of the **green curved path**

Moreover, his **displacement** will be the** length of a straight line** joining his **starting and ending point** in the specified direction(from starting to finish point)

You guys should be able to tell which arrow is representing distance and which is representing distance

**SPEED AND VELOCITY**

**Speed** is a **scalar quantity**. It is simply the total distance divided the total time taken to cover the distance. Since the concept of distance is already explained, speed should not be a problem.

**Velocity** is a **vector quantity**. It can be calculated by dividing displacement with time. We already laid down a strong foundation on the concept of displacement, Therefore, velocity should not be a problem. Just divide the displacement with the time taken.

**Mass and weight**

**MASS**

**Mass** is a **scalar quantit**y. That is, mass can be specified with **magnitude alone.**

**Mass can be defined as the quantity of matter/material in a body**. It should be noted that the mass of a body **does not change**, even when the body is taken to another planet be it the moon or Jupiter its mass remains constant.

**WEIGHT**

**Weight** is a vector quantity, Meaning to specify weight we need its magnitude and direction.

**Weight is defined as the gravitational pull on a body.** However, it should be noted that the weight of a body changes with the change in acceleration due to gravity

**W = mass * acceleration due to gravity**

It definitely means that for weight to change, the value of g must change.

Furthermore, the value of g is not constant even on earth. Please note that the value of g is higher at the pole compared with the equator.

The reason for this difference is because the distance between the center of the earth and the equator is larger when compared with the distance between the center of the earth and the pole.

**A more closer look at the reason why weight vary at different location**

Lets take a closer look at why the weight of a body can change.

**W = mg**

Everybody agrees with that formula. Since we are 100% sure that mass is constant and cannot change, it simply means for weight to change, **g **must be the changing factor.

Now, what is **g**?, where is** g **coming from?, how do we know that **g is 9.81m/s^{2}**

All this question will be answered right now.

**g** is popularly know as **acceleration due to gravity.**

Alternatively, **g **is known as **gravitational field intensity** or **gravitational field strength.**

Moreover, **g can also be defined as the force a unit mass will experience when under the influence of earth gravitational field.**

The famous **SIR ISAAC NEWTON ** postulated the **universal law of gravitation which is:**

“*The force of attraction between two bodies of masses m1 and m2 is directly proportional to the product of their masses and inversely proportional to the square of the distance between their center of mass*“

Mathematically, **F = \frac{G.m1.m2}{r^{2}}**

Now, lets m1 be m to represent the mass of a body on the earth surface.

Let m2 be M to represent the mass of the earth. Therefore, we can rewrite the above formula as:

F = \frac{G.m.M}{r^{2}}

This force **F is also equals to Weight** of the body.

Therefore, W = \frac{G.m.M}{r^{2}}

Since weight = mg; we can rewrite the formula to be:

**mg = \frac{G.m.M}{r^{2}}….**.eq(ii)

m is present in both side of the equation, let’s cancel them out so that we have;

**g = \frac{G.M}{r^{2}}**……eq(iii)

Finally i have what i want. Observing that formula carefully you will notice that acceleration due to gravity depends on the following:

**Gravitational constant, G**which has a value of**6.67408 × 10^{-11} m^{3} kg^{-1} s^{-2}****Mass of the earth**which has a value of**5.972 × 10^{24} kg****Radius of earth**which has an approximate value of**6,371 km**

Following equation(iii) it means that the value of **g will be constant if and only if the parameters G,M and r are constant.**

However, it is only **G and M that have a fixed value**. The radius of earth is not constant because the **earth is not perfectly spherical.**

Lets have a look at the shape of the earth

The earth isn’t perfectly spherical rather it is elliptical in shape as seen above

As you can see from the diagram above, the distance from the center of the earth to the equator(The yellow arrow) is quite large when compared with the distance from the center of the earth to the pole(White arrow).

Let **Re denote radius of equator** and **Rp denote radius of pole.**

since **g = \frac{G.M}{r^{2}}**

Therefore **ge** = **\frac{G.M}{Re^{2}}**

** gp = \frac{G.M}{Rp^{2}}**

ge is acceleration due to gravity at the equator

gp is acceleration due to gravity at the pole

since **Re >> Rp**, the value of gp will be greater than that of ge i.e ,**gp >> ge**

**The acceleration at the pole is about 9.83 m/s^{2} while at the equator it is about 9.78 m/s^{2}**

**Quiz Section**

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