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​ = 48N2​ = 16

A driving gear with 48 teeth turns at 1200 rpm and meshes with a gear with 16 teeth. Find the speed n2 of the driven gear.

N1 = 48N2 = 16n1 = 1200 rpm
n2 = rpm
2.Easy
N1​ = 80N2​ = 45

A driving gear with 80 teeth turns at 720 rpm and meshes with a gear with 45 teeth. Find the speed n2 of the driven gear.

N1 = 80N2 = 45n1 = 720 rpm
n2 = rpm
3.Medium
N1​ = 40N2​ = 48

A 2.2 kW motor running at 1500 rpm drives a pinion with 40 teeth, which meshes with a gear with 48 teeth. The gear pair has an efficiency of 98%. Find the torque T1 on the motor shaft.

P = 2.2 kWn1 = 1500 rpmN1 = 40N2 = 48η = 98%
T1 = N·m
4.Medium
N1​ = 16N2​ = 45

A 15 kW motor running at 1450 rpm drives a pinion with 16 teeth, which meshes with a gear with 45 teeth. The gear pair has an efficiency of 95%. Find the output torque T2 on the gear shaft.

P = 15 kWn1 = 1450 rpmN1 = 16N2 = 45η = 95%
T2 = N·m
5.Hard
A = 12B = 20C = 24D = 60

In a compound gear train, gear A (12 teeth) on the input shaft turning at 3000 rpm drives gear B (20 teeth). Gear C (24 teeth) is fixed to the same shaft as B and drives gear D (60 teeth) on the output shaft. Find the output speed nout.

nin = 3000 rpmA = 12B = 20C = 24D = 60
nout = rpm
6.Hard
d1​ = 80 mmd2​ = 300 mm2880 rpmC = 1000 mmT1​ = 800 NT2​P = ?

An open belt connects an 80 mm driving pulley at 2880 rpm to a 300 mm pulley; the centres are 1000 mm apart. The coefficient of friction is 0.3 and the tight-side tension may not exceed 800 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 80 mmn1 = 2880 rpmd2 = 300 mmC = 1000 mmμ = 0.3T1 = 800 N
P = kW

Answer key

  1. 1. n2 = 3600 rpm
  2. 2. n2 = 1280 rpm
  3. 3. T1 = 14.01 N·m
  4. 4. T2 = 263.9 N·m
  5. 5. nout = 720 rpm
  6. 6. P = 5.633 kW

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