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Convert mechanics quantities carefully, distinguish mass from weight, and check powers of units in speed, acceleration, area and density.
Before you startFractions, powers of ten and substitution.
01 / Keep the quantity and its unit together
Mass, length and time use kg, m and s in SI.
Force uses the newton, N. Weight is a force, so its unit is N, not kg. A quoted mass of 6 kg does not mean a weight of 6 N.
02 / Distinguish mass from force
State SI units for mass, displacement, time, velocity and acceleration.
Use metres and seconds to build compound units.
kg, m, s, m/s and m/s² respectively. Displacement, velocity and acceleration also require direction when fully specified.
A body has mass 6 kg. Using g=9.8 m/s², calculate its weight magnitude.
Weight magnitude W=mg.
W=6×9.8=58.8 N. The mass remains 6 kg.
Express one newton using kg, m and s.
Use force = mass × acceleration.
1 N=1 kg m/s².
03 / Convert the numerator and denominator
72 km/h = (72×1000) m / 3600 s
Convert both distance and time.
72×1000/3600 = 20 m/s
Equivalently, divide a km/h value by 3.6.
4 m/s = 4×3.6 = 14.4 km/h
The reverse conversion multiplies by 3.6.
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Convert 54 km/h to m/s.
Divide by 3.6.
54/3.6=15 m/s.
Convert 7.5 m/s to km/h.
Multiply by 3.6.
7.5×3.6=27 km/h.
Convert 150 cm/min to m/s.
Convert centimetres to metres, then minutes to seconds.
150 cm/min = 1.5 m/min = 1.5/60 = 0.025 m/s.
04 / Apply the power to the whole conversion
Convert 3 cm² to m².
1 cm=0.01 m; square the factor.
3×(0.01)²=0.0003 m² = 3×10⁻⁴ m².
Convert 8 cm³ to m³.
Cube the length factor.
8×(0.01)³=0.000008 m³ = 8×10⁻⁶ m³.
Convert 2 g/cm³ to kg/m³.
Convert the numerator and denominator separately.
2 g=0.002 kg and 1 cm³=10⁻⁶ m³. The density is 0.002/10⁻⁶=2000 kg/m³.
05 / Acceleration contains time squared
Convert 5 m/s² to cm/s².
Only the length unit changes here.
500 cm/s².
Convert 0.2 m/s² to m/min².
One minute contains 60 seconds; square the time factor.
0.2×60²=720 m/min². Acceleration is a change in velocity per time, so both occurrences of the time unit change.
06 / Check additions and products
If x is a length and t a time, what units must A and B have in x=A+Bt²?
Each term must have units of length.
A has units m and B has units m/s² when x and t use SI units.
Explain the problem with adding a mass directly to a distance.
Can the two terms represent the same kind of quantity?
They have different dimensions. The addition is not physically meaningful without a relation that first transforms them into comparable quantities.
07 / Use scale as a final check
A learner converts 72 km/h to 259.2 m/s by multiplying by 3.6. Explain the error.
Which direction uses multiplication?
Multiplication by 3.6 converts m/s to km/h. For km/h to m/s, divide by 3.6, giving 20 m/s. Writing 1000/3600 explicitly prevents the reversal.
Use units at intermediate stages, retain sufficient precision and check the size of the answer. A formula with matching dimensions can still use an unsuitable physical assumption or an incorrect dimensionless coefficient.
08 / Let the units guide the calculation
Mass uses kg; weight uses N. Convert km and hours independently for speed. Square or cube length factors for area and volume, and square the time factor for acceleration. Only add terms with the same dimensions.
Section 1 of 8 · Keep the quantity and its unit together