The user manual states an accuracy of 0.1% of the reading for a tachometer (an instrument measuring the rotation speed of a shaft or disk, as in a motor or other machine) with an analog display dial graduated in 5 revolutions per minute (rpm) increments. Estimate the design stage uncertainty at 5000 rpm.

the design stage uncertainty is ±5.6 rpm

Explanation:

Given that;

machine with an analog display dial graduated in 5 revolutions per minute (rpm) increments; Q = 5 rpm

now lets calculate zero order uncertainty in this machine

⇒ ± 1/2Q =  1/2(5) = ± 2.5 rpm

given that accuracy is 0.1% of reading

0.1% of 5000 rmp = 0.1/100 × 5000 = 5 rpm

now the design stage uncertainty at 5000 rpm will be;

⇒ √((5)² + (2.5)²)

= √(25 + 6.25)

= √ 31.25

= ±5.59 ≈ ±5.6 rpm

Therefore the design stage uncertainty is ±5.6 rpm

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