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​ = 80

A driving gear with 30 teeth turns at 1000 rpm and meshes with a gear with 80 teeth. Find the speed n2 of the driven gear.

N1 = 30N2 = 80n1 = 1000 rpm
n2 = rpm
2.Easy
N = 24, m = 2 mm

A gear with 24 teeth and a module of 2 mm turns at 1200 rpm. Find the pitch-line velocity v of its teeth.

N = 24m = 2 mmn = 1200 rpm
v = m/s
3.Medium
N1​ = 40N2​ = 45

A 5.5 kW motor running at 960 rpm drives a pinion with 40 teeth, which meshes with a gear with 45 teeth. The gear pair has an efficiency of 98%. Find the torque T1 on the motor shaft.

P = 5.5 kWn1 = 960 rpmN1 = 40N2 = 45η = 98%
T1 = N·m
4.Medium
Nw​ = 72z = 2, 1440 rpm

A worm with 2 start(s) turns at 1440 rpm and drives a worm wheel with 72 teeth. Find the speed nw of the wheel.

z = 2Nw = 72n = 1440 rpm
nw = rpm
5.Hard
A = 24B = 80C = 16D = ?

In a compound gear train, gear A (24 teeth) on the input shaft turns at 1500 rpm and drives gear B (80 teeth). Gear C (16 teeth) is fixed to the same shaft as B and drives gear D on the output shaft. The output must turn at 90 rpm. How many teeth ND must gear D have?

nin = 1500 rpmA = 24B = 80C = 16nout = 90 rpm
ND =
6.Hard
d1​ = 160 mmd2​ = 400 mm1440 rpmC = 500 mmθ = ?

An open belt connects a 160 mm pulley and a 400 mm pulley whose centres are 500 mm apart. Find the angle of wrap θ on the smaller pulley, in degrees.

d1 = 160 mmd2 = 400 mmC = 500 mm
θ = °

Answer key

  1. 1. n2 = 375 rpm
  2. 2. v = 3.016 m/s
  3. 3. T1 = 54.71 N·m
  4. 4. nw = 40 rpm
  5. 5. ND = 80
  6. 6. θ = 152.2 °

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