Theory of Measurements

Measurement of length and time accurate measurement There are two main types of errors: Random Errors Systematic Errors Staterandomconstant Occurrence in all measurements observers estimate the last figure of a reading on an instrument observers consistently underestimate or overestimate a reading Remedy reduced by averaging a large number of readings minimized by method of differences No measurement is ever perfectly accurate. Even with high precision instruments, some error is inevitable.

One meter is the distance travelled by light in a vacuum in 1/ of a second. Measurement of length length Length is the measurement of something from one end to the other end.  has a SI unit of meter (m)  other units include centimeters (cm), millimeters (mm) and kilometers (km)  has a SI unit of meter (m)  other units include centimeters (cm), millimeters (mm) and kilometers (km)

Measurement of length length  measuring tape accuracy = 1 mm / 0.1 cm / m Lengths can be measured by using the following: accuracy = 1 mm / 0.1 cm / m  metre/half-metre rule

Measurement of length Parallax error is due to  incorrect positioning of the eye  the object is not at the same level as the markings of the scale Parallax error is due to  incorrect positioning of the eye  the object is not at the same level as the markings of the scale parallax error 8.5 cm wrong 8.2 cm wrong 8.3 cm correct The eye must be positioned perpendicularly at the mark on the scale to avoid parallax error.

Measurement of length Zero error Many instruments do not read zero exactly when there is nothing being measured. Reasons include: Many instruments do not read zero exactly when there is nothing being measured. Reasons include:  instruments are out of adjustment  some minor fault is present in the instrument  instruments are out of adjustment  some minor fault is present in the instrument Instruments are usually still accurate as long as the zero error is added or subtracted from the reading shown on the scale.

Engineer’s calipers A pair of engineer’s calipers and ruler are used for measuring the lengths of objects without any flat sides. Measurement of length the jaws are closed until the points just touch the object to be measured remove the calipers and measure the distance between the jaws with a ruler.

Vernier calipers measure small lengths accurately up to 0.01 cm. Vernier calipers Measurement of length Accuracy = 0.1 mm / 0.01 cm inside jaws outside jaws main scalevernier scale tail

reading on main scale (between A and B) = 2.4 cm reading on vernier scale (C) = 0.08 cm actual reading of object = = 2.48 cm vernier calipers Measurement of length main scale (fixed) vernier scale (movable) object being measured AB C 9 mm

Vernier calipers Measurement of length When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide. If not, there is a zero error in the vernier calipers. When the two jaws of the vernier calipers touch each other, both zero marks on the main scale and on the vernier scale should coincide. If not, there is a zero error in the vernier calipers.

supposing observed reading is 3.24 cm, then corrected reading = observed reading – zero error = 3.24 – (+0.01) = 3.23 cm Measurement of length zero error = cm main scale (fixed) vernier scale (movable) 01 If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is positive. Vernier calipers

supposing observed reading is 4.03 cm, then corrected reading = observed reading – zero error = 4.03 – (-0.02) = 4.05 cm Measurement of length 010 zero error = cm main scale (fixed) vernier scale (movable) 01 If the two jaws touch each other, but the zero marks of the main scale and vernier scale do not coincide as shown below, the zero error is negative. 5 Vernier calipers

Micrometer screw gauge Measurement of length Accuracy = 0.01 mm / cm anvilspindlesleevethimbleratchet frame Micrometers measure small diameters or thicknesses.

micrometer screw gauge measurement of length reading on sleeve = 4.5 mm reading on thimble = 0.12 mm actual reading of object = = 4.62 mm thimble sleeve

Measurement of length Micrometer screw gauge When the anvil and spindle of the micrometer touch each other, the scales should read zero. If not, there is a zero error in the micrometer. When the anvil and spindle of the micrometer touch each other, the scales should read zero. If not, there is a zero error in the micrometer.

measurement of length micrometer screw gauge If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is positive. supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error = 2.37 – (+0.02) = 2.35 mm supposing observed reading is 2.37 mm, then corrected reading = observed reading – zero error = 2.37 – (+0.02) = 2.35 mm } 2 divisions

Measurement of length Micrometer screw gauge If the anvil and spindle touch each other, but the scales do not read zero as shown below, the zero error is negative. supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03) = 2.90 mm supposing observed reading is 2.87 mm, then corrected reading = observed reading – zero error = 2.87 – (-0.03) = 2.90 mm } 3 divisions

Measurement of time Time  has a SI unit of second (s)  other units include years, months, days, hours, minutes and seconds  has a SI unit of second (s)  other units include years, months, days, hours, minutes and seconds

Measurement of time Time can be measured by using the following:  analogue stopwatch  digital stopwatch  clocks All timing devices make use of some regular process. Time

Measurement of time Time can also be measured by using the following simple pendulum.  oscillations are regularly repeating motions  the period is time in which 1 oscillation occurs  oscillations are regularly repeating motions  the period is time in which 1 oscillation occurs The period of a simple pendulum pendulum bob tied to one end of a thread BA O

A stopwatch is used to measure short intervals of time. Stopwatch accuracy = 0.1 saccuracy = 0.01 s measurement of time  stopwatches (analogue and digital) When using a digital stopwatch to time a race, the time to the nearest 0.1 s should be given.

Ticker-tape timer Measurement of time An electrical device that makes use of the oscillations of a steel strip to mark short intervals of time. steel strip magnetcoilticker-tapedrawing pin carbon paper disc6 ~ 12 V a.c.

Ticker-tape timer Measurement of time 10-dot tape as there are 10 spaces on a piece of tape, time taken for the tape to pass through the timer = 10 x 0.02 s = 0.20 s between 2 consecutive dots, time interval = 1 s / 50 dots = (1/50) s or 0.02 s  steel strip vibrates 50 times a second; therefore 50 dots are made in a second on the paper tape

e.g. metre rule half-metre rule measuring tape vernier calipers micrometer screw gauge pendulum clock watchstopwatch ticker-tape timer length (m) mass (kg) time(s) electric current (A) temperature (K) amount of substance (mol) luminous intensity (cd) PrefixesMeasurement Physical quantities are made up of can be measured with e.g. of Numerical values and suitable units VectorScalar Base quantities Base SI units Time Length micro () milli (m) centi (c) deci (d) kilo (k) 10 3 mega (M) 10 6 may be include usesuch asfor can be measured with