# 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 Displacement 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 quantities
• 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 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 distance 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 quantity. 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 9.81$m/s^{2}$

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

You can check out your understanding of this topic by clicking the button below to take the quiz

Philip Obhenimen

Hello world, first I want to thank you for visiting my blog and hope you find the content useful. My name is JOHN PHILIP OBHENIMEN the CEO of poschools.com I am currently studying mechanical engineering in a reputable university. I am very passionate about educating young people on academics,career and skill acquisition. I pray that the Almighty God help assists me in accomplishing the above.

### 15 Responses

Boss phillip there… More grace bro

1. February 17, 2019

[…] My Jamb tutorials on physics (Vectors and scalars) […]

2. February 17, 2019

[…] Check my jamb tutorial on Scalars and vector […]

3. February 17, 2019

[…] Check out myJamb Physics tutorial on Scalars and vectors […]

4. February 17, 2019

[…] Jamb tutorials on Scalars and Vectors […]

5. February 17, 2019

[…] Check out my physics tutorial on Scalars and vectors […]

6. February 18, 2019

[…] However, if you get below 60%, its not the end of the road dear, I will recommend you check out the tutorial I made on Measurement and units for Jamb physics by clicking here […]

7. February 22, 2019

[…] Visit my Jamb online S02 tutorials here […]

8. February 23, 2019

[…] Visit my Jamb physics online S02 tutorials here […]

9. February 23, 2019

[…] Visit my Jamb physics online S02 tutorials here […]

10. March 2, 2019

[…] Check out my Jamb physics tutorial S02 […]

11. March 3, 2019

[…] Visit my Jamb physics online S02 tutorials here […]

12. March 3, 2019

[…] Visit my Jamb physics online S02 tutorials here […]

13. March 10, 2019

[…] Visit my Jamb physics online S02 tutorials here […]

14. March 11, 2019

[…] Visit my Jamb physics online S02 tutorials here […]