Introduction to Physics and Measurement of Physical Quantities
Senior 1 · Physics
Introduction to Physics and Measurement of Physical Quantities
Lesson 3 of 5
25 min
Try to measure the thickness of one page of your exercise book with a ruler. You cannot: the page is far thinner than the smallest division on the ruler, 1 mm. Yet a mechanic in a garage in Kigali needs to know whether a bolt is 8.00 mm or 7.96 mm thick, and a carpenter at Gisozi needs to cut a door frame to the nearest millimetre.
Each job needs the right instrument. In this lesson you will learn to choose and read four of them: the tape measure, the metre rule, the vernier caliper and the micrometer screw gauge.
Definition
Length is the distance between two points. Its SI unit is the metre (m).
The least count (or precision) of an instrument is the smallest length it can measure, usually its smallest scale division. A metre rule has a least count of 1 mm .
Place the ruler flat, right against the object. Read both ends and subtract. Many old rulers have a worn or damaged zero end, so it is safer to start at a clear mark such as 1.0 cm or 2.0 cm.
Figure 3.1: The pencil starts at 2.0 cm and ends at 7.4 cm, so its length is 7.4 cm minus 2.0 cm, which is 5.4 cm. Only the eye directly above the end gives the true reading.
Definition
Parallax error is the error made when a scale is read with the eye at an angle instead of straight on, because the object and the scale are not in exactly the same plane.
Warning
Avoid parallax: always put your eye directly above (or directly level with) the mark you are reading. In Figure 3.1 an eye too far to the left reads 7.8 cm and an eye too far to the right reads 7.0 cm, although the pencil ends at 7.4 cm.
A vernier caliper has a main scale marked in millimetres and a sliding vernier scale. On a common school caliper the vernier has 10 divisions that together span 9 mm, so each vernier division is 0.9 mm, 0.1 mm shorter than a main-scale division. That difference, 0.1 mm or 0.01 cm, is the least count.
It has outside jaws for external sizes (the diameter of a pipe or a bolt), inside jaws for internal sizes (the inside of a cup or a test tube) and a depth rod for the depth of a hole.
Figure 3.2: The vernier zero is just past 2.4 cm on the main scale, and vernier line 7 lines up with a main-scale line, so the reading is 2.47 cm.
Worked example 1: reading a vernier caliper
Read the caliper in Figure 3.2.
Main scale, just before the vernier zero: 2.4 cm. Vernier line lining up: line 7.
For very small sizes, such as the diameter of a wire or the thickness of a sheet of metal, use a micrometer screw gauge. Turning the thimble once moves the spindle forward by 0.5 mm (its pitch). The thimble has 50 divisions, so one division is
Figure 3.3: The sleeve shows 5 mm and the half-millimetre mark after it, so 5.5 mm. Thimble line 28 is on the datum line, adding 0.28 mm. The reading is 5.78 mm.
Worked example 2: reading a micrometer
Read the micrometer in Figure 3.3.
Worked example 3: correcting a zero error
When the jaws of a vernier caliper are closed with nothing between them, it reads 0.03 cm instead of zero. A block then gives a reading of 3.42 cm. What is the true length?
The caliper adds 0.03 cm to every reading, a zero error of . Subtract it:
If the zero error were negative, for example , subtracting it would ADD 0.02 cm.
Definition
A zero error is the reading an instrument gives when it should read zero. Always check it before measuring, and correct each reading: true value = reading − zero error.
| Instrument | Least count | Typical range | Good for |
|---|---|---|---|
| Tape measure | 1 mm or 1 cm | up to 30 m or more | a room, a plot of land, a football pitch |
| Metre rule | 1 mm | up to 1 m | a desk, a book, a pendulum string |
| Vernier caliper | 0.1 mm (0.01 cm) | up to about 15 cm | diameters of pipes and bolts, the inside of a test tube, depths of holes |
| Micrometer screw gauge | 0.01 mm | up to 25 mm | diameter of a wire, thickness of a sheet or a coin |
Back to the page of your exercise book. Squeeze 100 sheets together and measure the stack: say 8.0 mm. Then one sheet is . Measuring many and dividing is the same trick you used to time many swings of a pendulum.
Tip
Main first, then the match. For both instruments, read the main scale (or sleeve) first, then find the line that matches (vernier) or sits on the datum (thimble), multiply by the least count and add.
Carpenters and builders use tape measures and folding rules to set out walls and cut timber. In the mechanical workshops of Rwanda Polytechnic colleges, trainees use vernier calipers and micrometers to check that engine parts and bolts are the right size, often to a hundredth of a millimetre. Electricians choose cable by the size of its copper wire, and a micrometer is one way to check a wire's diameter.
How to Use a Vernier Caliper (SMUPhysics). Watch how the reading is built from the main scale and the one vernier line that lines up, then check it with the steps above.
Practice
Key points
Sources and credits
Written by Ganzaa: the lesson text, the diagrams, the worked examples and the practice exercises.
