Workshop Calculation and Science
Workshop Calculation and Science
This domain tests the arithmetic and applied science used for measurement, material estimation, and machine setting. Expect unit conversion, percentage, ratio, mensuration, density, and cutting-speed calculations.
Core rules
- Use SI units consistently: 1 m = 1000 mm; 1 cm² = 100 mm²; 1 litre = 1000 cm³.
- Area of rectangle = length × breadth; circle area = πr²; volume of a block = l × b × h.
- Density = mass/volume; percentage change = (change/original) × 100.
- For turning or drilling, spindle speed N (rpm) ≈ 1000S/(πD), where S is cutting speed in m/min and D is diameter in mm.
- Round up when buying whole pieces; round to the required precision only at the final step.
Worked example
A drill of 20 mm diameter is to run at a cutting speed of 25 m/min. N = 1000 × 25/(π × 20) = 25,000/62.83 ≈ 398 rpm. A benchtop drill with stepped speeds would be set to the nearest available speed below or at 398 rpm, depending on the material and coolant advice. If the diameter is doubled to 40 mm, speed halves to about 199 rpm-larger diameter means lower rpm for the same surface speed. The reasoning is that surface speed depends on circumference, so a larger circle travels further per revolution.
Traps
Mixing millimetres and metres in the same formula; forgetting π; using diameter instead of radius in area; and rounding down when a whole number of pieces is required.