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

A 120 mm pulley turns at 720 rpm. Find the belt speed v in m/s.

d₁ = 120 mmn₁ = 720 rpm

v = m/s

2.Easy

A driving gear with 24 teeth turns at 1440 rpm and meshes with a gear with 45 teeth. Find the speed n₂ of the driven gear.

N₁ = 24N₂ = 45n₁ = 1440 rpm

n₂ = rpm

3.Medium

A belt runs on a 160 mm driving pulley at 720 rpm. The tension is 400 N on the tight side and 200 N on the slack side. Find the power P transmitted, in kW.

d₁ = 160 mmn₁ = 720 rpmT₁ = 400 NT₂ = 200 N

P = kW

4.Medium

A 120 mm pulley at 1440 rpm drives a 450 mm pulley by a belt with 1.5 % slip. Find the speed n₂ of the driven pulley.

n₁ = 1440 rpmd₁ = 120 mmd₂ = 450 mms = 1.5 %

n₂ = rpm

5.Hard

A 4 kW motor at 1440 rpm drives gear A (18 teeth), which meshes with gear B (50 teeth). Gear C (60 teeth) on the same shaft as B drives gear D (80 teeth) on the output shaft. Each gear mesh has an efficiency of 95%. Find the output torque T_out.

P = 4 kWn_in = 1440 rpmA = 18B = 50C = 60D = 80η_mesh = 95%

T_out = N·m

6.Hard

In a compound gear train, gear A (24 teeth) on the input shaft turning at 1500 rpm drives gear B (32 teeth). Gear C (12 teeth) is fixed to the same shaft as B and drives gear D (60 teeth) on the output shaft. Find the output speed n_out.

n_in = 1500 rpmA = 24B = 32C = 12D = 60

n_out = rpm

Answer key

1. v = 4.524 m/s
2. n₂ = 768 rpm
3. P = 1.206 kW
4. n₂ = 378.2 rpm
5. T_out = 88.67 N·m
6. n_out = 225 rpm

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