Measurements

Measuring is a process of the object in SI Unit.

Uncertainty

Uncertainty is the uncertain of the Measurement.

To find the Uncertainty in Vernier Caliper and Micrometer use this Formula :

▲X = ½ * Smallest Scale

Examples :

Vernier Caliper's Smallest Scale is 0.1 thus ▲X = ½ * 0.1 = 0.05 mm

Micrometer's Smallest Scale is 0.01 thus ▲X = ½ * 0.01 = 0.005 mm

Vernier Caliper

Look at the Picture. To read its Measurement first look at the Measurement of the First Scale. It stops at 10 cm. Then look at the Second Scale find the scale which is Aligned. Its 2 so its 0.2 cm.
Then sum it up 10.2 cm ± (Uncertainty) Which is 0.05 mm

Micrometer

Look at the Picture. To read its Measurement first look at the Measurement of the First Scale. It stops at 2.5 mm. Then look at the Second Scale fine the scale which is Aligned at the Picture. Its 12 so its 0.12 mm.

Then sum it up 2.62 mm ± (Uncertainty) Which is 0.005 mm

Another way to find Uncertainty is using this Formula :

1 ÷ N √((N(ΣI²) - (ΣI)²) ÷ (N - 1))

Example : (All in kg)

N                   I                   I²

1                   1                  1

2                   2                  4

3                   3                  9

4                   4                  16

5                   5                  25

1 ÷ 5 * √((5(55) - (15)²) ÷ (5 - 1)) = 1 ÷ 5 * √((275 - 225) ÷ 4) = 1 ÷ 5 * √(50 ÷ 4)

= 1 ÷ 5 * √12.5 ≈ 1 ÷ 5 * 3.54 ≈ 0.88 kg

Then find the Average of ΣI which is 15 ÷ 5 = 3 kg

Then the report of  the measurement is 3 kg ± 0.88 kg

To find the Accuracy use this Formula :

Uncertainty ÷ Average of ΣI * 100

Example :

0.88 ÷ 3 * 100 = 29%

Dimension

Dimension is an expression of the character of a derived quantity in relation to fundamental quantities, without regard for its numerical value.

Base Quantity                                         Dimension

Length                                                           L

Mass                                                             M

Time                                                              T

Current                                                          I

Temperature                                                 Θ (tetha)

Light Intensity                                               J

Number of Substance                                   N

Examples :

Normal Gravity is Meter / Second² so its [L] [T]^-2

Force is Mass * Meter / Second² so its [M] [L] [T]^-2

Work is Mass * Meter / Second² * Length so its [M] [L]² [T]^-2

Power is Mass * Meter / Second² * Length ÷ Second so its [M] [L]² [T]^-3

Sound Intensity is (Mass * Meter / Second² * Length ÷ Second) ÷ Meter² so its [M] [T]^-3