Gears & gear trains worksheet with answers

Free printable Gears & gear trains worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
N1​ = 30N2​ = ?

A pinion with 30 teeth is driven at 2400 rpm. The driven gear must turn at 1800 rpm. How many teeth N2 must the driven gear have?

N1 = 30n1 = 2400 rpmn2 = 1800 rpm
N2 =
2.Easy
d1​ = 120 mmd2​ = 250 mm2880 rpmv = ?

A 120 mm pulley turns at 2880 rpm. Find the belt speed v in m/s.

d1 = 120 mmn1 = 2880 rpm
v = m/s
3.Medium
N1​ = 20N2​ = 32

A 1.5 kW motor running at 2900 rpm drives a pinion with 20 teeth, which meshes with a gear with 32 teeth. The gear pair has an efficiency of 97%. Find the torque T1 on the motor shaft.

P = 1.5 kWn1 = 2900 rpmN1 = 20N2 = 32η = 97%
T1 = N·m
4.Medium
Nw​ = 80z = 2, 1440 rpm

A worm with 2 start(s) turns at 1440 rpm and drives a worm wheel with 80 teeth. Find the speed nw of the wheel.

z = 2Nw = 80n = 1440 rpm
nw = rpm
5.Hard
A = 18B = 48C = 45D = 48

In a compound gear train, gear A (18 teeth) on the input shaft turning at 3000 rpm drives gear B (48 teeth). Gear C (45 teeth) is fixed to the same shaft as B and drives gear D (48 teeth) on the output shaft. Find the output speed nout.

nin = 3000 rpmA = 18B = 48C = 45D = 48
nout = rpm
6.Hard
d1​ = 125 mmd2​ = 300 mm720 rpmC = 600 mmθ = ?

An open belt connects a 125 mm pulley and a 300 mm pulley whose centres are 600 mm apart. Find the angle of wrap θ on the smaller pulley, in degrees.

d1 = 125 mmd2 = 300 mmC = 600 mm
θ = °

Answer key

  1. 1. N2 = 40
  2. 2. v = 18.1 m/s
  3. 3. T1 = 4.939 N·m
  4. 4. nw = 36 rpm
  5. 5. nout = 1055 rpm
  6. 6. θ = 163.2 °

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