The Screw Gauge

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Your vernier callipers have a least count of zero point one millimetre. Now I give you a thin wire, and I ask you for its diameter. Zero point one millimetre, for a wire that thin. Is that good enough? Not really, right? We need an instrument about ten times finer. And look, the secret behind it is something very ordinary: a simple screw. Today we learn the screw gauge, its least count, and how to take a reading. In JEE, this is a must know skill. So, let's begin.

0:38One full turn of the screw: the pitch

So, here is a screw gauge. The object sits between the anvil and the spindle. Then comes the main scale, also called the linear scale, with a long line along it: the index line. And the thimble carries a circular scale, with the ratchet at the far end. Clear? Now the big idea. Turn a screw by one full turn, and it moves forward by a fixed distance. This fixed distance is called the pitch of the screw. Simple, right? Alright, so how do we find the pitch? We turn the screw a few full rotations, and see how far it moved on the main scale. Now tell me: is that distance the pitch? No, no! That is the distance for many turns, and the pitch is for one turn only. So, divide. Pitch equals the distance moved on the main scale, divided by the number of full rotations. Distance per turn, as simple as that. Now look at the head of the screw, the thimble. It carries a circular scale with N equal divisions, okay? Now think. One full turn moves the screw by one pitch. So if I turn the head by just one division, that is, one by N of a turn, how far does the screw move? Got it? Yes, exactly! One division moves it by the pitch, divided by N, okay? This tiny distance is the heart of the screw gauge.

2:06Least count of a screw gauge

And that tiny distance is exactly the least count of the screw gauge, written L C on screen. The least count equals the pitch, divided by the number of circular divisions. Write this down. Got it? Let's put in some typical numbers. Pitch zero point five millimetre, and fifty divisions. Zero point five divided by fifty: zero point zero one millimetre. Pitch one millimetre, and one hundred divisions. One divided by one hundred: again, zero point zero one millimetre. Exactly the same least count. Now you tell me. Keep the pitch at zero point five millimetre, but cut the circle into one hundred divisions instead of fifty. Does the least count get finer, or coarser? Finer, that's right! Zero point five divided by one hundred: zero point zero zero five millimetre. More divisions, smaller least count. Now back to our thin wire. Vernier callipers read to zero point one millimetre. The screw gauge reads to about zero point zero one millimetre. That is the ten times finer we wanted! And why does it work? Because a small pitch is divided into many circular divisions. So, for the diameter of a thin wire, you pick the screw gauge. Got it?

3:28Taking a reading

Alright, now the reading. Reading equals the main scale reading, plus the circular scale reading times the least count. On screen, MSR is the main scale reading, and CSR is the circular scale reading, okay? And then, minus the zero error, if the gauge has one. Zero error gets its own lesson. For now, take it as zero, okay? Now, which number is the circular scale reading? Look at the index line on the main scale. The circular scale division lying on that line: that is your circular scale reading. Look at the figure. Division thirty two of the circular scale is on the index line. So, we add thirty two millimetres to the reading, right? Oh no, no, no! Careful! Thirty two is a count of divisions, not millimetres. Each division is worth one least count. So, with a least count of zero point zero one millimetre, thirty two divisions give thirty two times zero point zero one: zero point three two millimetre. Always multiply by the least count first.

4:35Example 1: reading a screw gauge of pitch 1 mm

Clear? Now, example one. The pitch of a screw gauge is one millimetre, and its circular scale has one hundred divisions. The main scale reads three millimetres, and division forty five is on the line. There is no zero error. Find the reading. Pause the video, and try it first. Done? Okay, let's check. Step one, always: the least count. Pitch over divisions: one millimetre divided by one hundred, that is zero point zero one millimetre. Step two: the circular part. Forty five divisions, each worth zero point zero one millimetre. Forty five times zero point zero one: zero point four five millimetre. Not forty five millimetres, right? Step three: add the main scale reading, and subtract the zero error, which is zero here. Three plus zero point four five: three point four five millimetres. That's it, done!

5:37Example 2: divisions needed for a 2 micrometre least count

Now a slightly harder one. Here, the question is turned around. The screw has a pitch of zero point five millimetre. How many circular divisions are needed for a least count of two micrometres? The symbol mu on screen means micro. Pause the video, and try it. Done? Okay, let's check. Here is a topper's trick. Least count equals pitch over N, so turn it around: N equals the pitch, divided by the least count. Know any two, and you get the third, okay? So, zero point five divided by two. Zero point two five divisions, right? Hmm, a quarter of a division? That can't be right, can it? This is the trap. The pitch is in millimetres, but the least count is in micrometres. So, same units first. Two micrometres is zero point zero zero two millimetre. With me? Now divide. Zero point five millimetre, divided by zero point zero zero two millimetre. Two hundred and fifty divisions! Quick check: zero point five divided by two hundred and fifty gives back zero point zero zero two millimetre. Absolutely correct.

6:52Quick revision: pitch, least count and reading

So, quick revision. Pitch is the distance the screw moves in one full turn. Least count is the pitch, divided by the number of circular divisions: small pitch, many divisions, fine least count. And the reading is the main scale reading, plus the circular scale reading times the least count, minus the zero error. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!