Physical Quantities, Units and Systems of Units

Transcript

0:00Introduction

Hello everyone! Before we start, one small puzzle. I measure a rod and tell you: two point five. My friend measures the same rod and says: two hundred and fifty. And a third friend says: zero point zero zero two five. One rod, three different numbers. So, who is right? Well, maybe all three of us! Hold on to that thought. Because this is the very first idea of physics. Almost every answer you write in JEE physics comes with a unit. Come on, let's begin.

0:34Physical quantity = number × unit

So, first question. If I say, this rod is long, is that physics? No! Long compared to what? Your long and my long can be totally different, right? But if I say, the rod is two point three five metres long, now that is physics. Anything that can be measured and written as a number is a physical quantity: length, mass, time, speed, force, charge, temperature. Now, how do we measure? We compare the quantity with a fixed reference of the same kind, and that reference is called a unit. So every measurement is written as Q equals n times u, okay? Here u is the unit, and n is the numerical value: how many units fit into the quantity. For example, five metres. The number n is five, and the unit u is the metre. Number times unit. Simple, isn't it?

1:29Change the unit: only the number changes

Alright, now back to our rod. When I change the unit, does the rod become longer or shorter? Of course not! The rod stays exactly the same; only the number changes. So for the same quantity in two units, n one times u one equals n two times u two, okay? Now tell me. If I make the unit bigger, the number also becomes bigger, right? No, no, careful! This is exactly where students slip. Look at the equation again. If u goes up, n must come down, so that the product stays the same. So n is proportional to one over u; that curly sign on screen means proportional to. Bigger unit, smaller number. Exactly. See, one kilometre equals one thousand metres. The bigger unit, the kilometre, carries the small number, one. The smaller unit, the metre, carries the big number, one thousand. Same distance, got it?

2:27Base and derived quantities

Next, base and derived quantities. We choose a small set of quantities as base quantities, also called fundamental quantities. Their units are defined independently, okay? Every other quantity is a derived quantity. Its unit is built from the base units, like a wall built from bricks. So tell me, what is the unit of speed? Yes, speed is length divided by time. So its unit is metre per second, written on screen as metre second to the power minus one, okay? Built from the metre and the second, both base units.

3:01Systems of units

Now, which units do we use for length, mass and time? You see, there are different systems. In the CGS system, we use the centimetre, the gram and the second. The name is just the first letters of these three units. Simple, right? Next, the FPS system, the British one: the foot, the pound and the second. Same idea, first letters again. Clear? And in the MKS system: the metre, the kilogram and the second. The S I system, in use since nineteen seventy one and revised in twenty nineteen, uses these same three for mechanics. But it adds four more base quantities. Which four? Let's see.

3:44The seven SI base quantities

So, the S I system has seven base quantities. The first three come from mechanics: length in metre, symbol small m; mass in kilogram, k g; and time in second, small s, okay? Then two more: electric current, in ampere, symbol capital A, and thermodynamic temperature, in kelvin, capital K, okay? And the last two: amount of substance, in mole, written m o l, and luminous intensity, in candela, written c d, okay? That's all, just seven. Easy way to remember: three plus four. The three of mechanics, plus current, temperature, amount of substance and light. And what about angles? Plane angle, in radian, r a d, and solid angle, in steradian, s r, are dimensionless derived units. Older books call them supplementary units. So they are not among the seven base units, okay?

4:44Since 2019: each base unit fixed by a constant

Since twenty nineteen, every S I base unit is defined by fixing the exact value of a constant of nature. Read each arrow on screen as, fixes. The second is fixed by the caesium one thirty three frequency, the delta nu you see on screen. And the metre by the speed of light, c, together with the second, okay? Planck's constant, h, fixes the kilogram. And the elementary charge, e, fixes the ampere. Makes sense, right? Charge and current go together. Boltzmann's constant, k B, fixes the kelvin. And Avogadro's number, N A, fixes the mole, okay? And last, the candela is fixed by the luminous efficacy, K c d, of light of one particular frequency. Now, for JEE you do not need the digits of these constants. But questions do ask which constant fixes which unit. So learn these pairs.

5:43JEE traps: base quantity or not?

Now for the traps. Charge feels so basic. Surely it is a base quantity, right? No, no, careful! In S I, current is the base quantity, and charge is derived. One coulomb equals one ampere into one second, okay? So the coulomb is not a base unit. Write this down. Same trap with heat. Temperature is a base quantity, but heat is not, because heat is energy, okay? And the most common one. In daily life we say, my weight is so many kilograms, don't we? But in physics, weight is a force, so it is measured in newton, not in kilogram. Got it?

6:23Example 1: a 2.5 m rod in centimetre and kilometre

Now let's settle our puzzle. The rod is two point five metres long. Express its length in centimetre and in kilometre, and check that n is proportional to one over u. Pause the video, and try it first. Done? Okay, let's check. Two point five metres is two hundred and fifty centimetres. The centimetre is a hundred times smaller than the metre, so the number is a hundred times larger, okay? Now the kilometre. It is a thousand times larger than the metre, so the number becomes a thousand times smaller: two point five into ten to the power minus three kilometre. That is the zero point zero zero two five of our third friend! So who was right? All three of us. Same rod, different units. Crystal clear, right?

7:14Example 2: newton to dyne and joule to erg

Now a harder one, JEE level. Express one newton in dyne, the CGS unit of force, and one joule in erg, the CGS unit of energy. Pause and try. Hint: write each unit in base units first. Done? Okay, let's check. Here is the topper's trick for any conversion: break the unit into base units, then replace each base unit. One newton is one kilogram metre per second squared. Put in one thousand grams for the kilogram, and one hundred centimetres for the metre. Thousand into hundred is ten to the power five. So one newton is ten to the power five dyne, okay? Alright, now the joule: one kilogram metre squared per second squared. Same thousand, same hundred. So again ten to the power five erg, right? No, no, careful! Look at the metre. It is squared. So the hundred centimetres also gets squared, and hundred squared is ten to the power four. Thousand into ten to the power four is ten to the power seven. One joule is ten to the power seven erg. Forget that square, and you lose the marks. Clear?

8:27Quick revision: n1u1 = n2u2 and the seven SI base units

So, quick revision. Quantity equals number times unit, and a bigger unit gives a smaller number. There are seven S I base quantities; charge, heat and weight are not among them. And since twenty nineteen, each base unit is fixed by a constant of nature. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!