Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
k = 0.2 m0 → 1800 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1800 rpm. This takes 22 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.2 mn1 = 0 rpmn2 = 1800 rpmt = 22 s
T = N·m
2.Easy
k = 0.1 m700 → 2000 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.1 m is accelerated uniformly from 700 rpm to 2000 rpm. This takes 18 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.1 mn1 = 700 rpmn2 = 2000 rpmt = 18 s
T = N·m
3.Medium
L = 0.8 mm = 7.5 kgα

A uniform slender rod of mass 7.5 kg and length 0.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 7.5 kgL = 0.8 mg = 9.81 m/s²
α = rad/s²
4.Medium
8 kgaαM = 14.5 kgR = 0.1 m

An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 14.5 kg and radius 0.1 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 8 kgM = 14.5 kgR = 0.1 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 30°vs = 7 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.4 m. Find its angular velocity ω after it has rolled 7 m along the slope.

θ = 30°s = 7 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.4 m
ω = rad/s
6.Hard
θ = 35°a

A hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 35°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. T = 41.13 N·m
  2. 2. T = 9.076 N·m
  3. 3. α = 18.39 rad/s²
  4. 4. α = 51.46 rad/s²
  5. 5. ω = 16.05 rad/s
  6. 6. a = 3.376 m/s²

Full step-by-step solutions: practise this topic on examproblems.com.