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​ = 25N2​ = 50

A driving gear with 25 teeth turns at 1500 rpm and meshes with a gear with 50 teeth. Find the speed n2 of the driven gear.

N1 = 25N2 = 50n1 = 1500 rpm
n2 = rpm
2.Easy
N1​ = 16N2​ = ?

A pinion with 16 teeth is driven at 2400 rpm. The driven gear must turn at 2560 rpm. How many teeth N2 must the driven gear have?

N1 = 16n1 = 2400 rpmn2 = 2560 rpm
N2 =
3.Medium
N1​ = 18N2​ = 50

A 1.1 kW motor running at 2900 rpm drives a pinion with 18 teeth, which meshes with a gear with 50 teeth. The gear pair has an efficiency of 97%. Find the output torque T2 on the gear shaft.

P = 1.1 kWn1 = 2900 rpmN1 = 18N2 = 50η = 97%
T2 = N·m
4.Medium
d1​ = 100 mmd2​ = 400 mm720 rpmT1​ = 1500 NT2​ = 300 NP = ?

A belt runs on a 100 mm driving pulley at 720 rpm. The tension is 1500 N on the tight side and 300 N on the slack side. Find the power P transmitted, in kW.

d1 = 100 mmn1 = 720 rpmT1 = 1500 NT2 = 300 N
P = kW
5.Hard
A = 24B = 25C = 40D = 60

In a compound gear train, gear A (24 teeth) on the input shaft turning at 1450 rpm drives gear B (25 teeth). Gear C (40 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 = 1450 rpmA = 24B = 25C = 40D = 60
nout = rpm
6.Hard
d1​ = 125 mmd2​ = 315 mm720 rpmC = 500 mmT1​ = 2000 NT2​P = ?

An open belt connects a 125 mm driving pulley at 720 rpm to a 315 mm pulley; the centres are 500 mm apart. The coefficient of friction is 0.25 and the tight-side tension may not exceed 2000 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 125 mmn1 = 720 rpmd2 = 315 mmC = 500 mmμ = 0.25T1 = 2000 N
P = kW

Answer key

  1. 1. n2 = 750 rpm
  2. 2. N2 = 15
  3. 3. T2 = 9.76 N·m
  4. 4. P = 4.524 kW
  5. 5. nout = 928 rpm
  6. 6. P = 4.697 kW

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