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
R = 0.65 mn = 2700 rpm220 kg

A flywheel is a uniform solid disc of mass 220 kg and radius 0.65 m. It spins at 2700 rpm. Find its kinetic energy Ek in kJ.

M = 220 kgR = 0.65 mn = 2700 rpm
Ek = kJ
2.Easy
L = 2.4 mGOd = 0.35 mm = 1 kg

A uniform slender rod of mass 1 kg and length 2.4 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1 kgL = 2.4 md = 0.35 m
IO = kg·m²
3.Medium
v = ?L = 1.7 mm = 4 kg

A uniform slender rod of mass 4 kg and length 1.7 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 4 kgL = 1.7 mg = 9.81 m/s²
v = m/s
4.Medium
n = 1300 rpmT = 970 N·m

A motor delivers a torque of 970 N·m at 1300 rpm. Find its power output P in kW.

T = 970 N·mn = 1300 rpm
P = kW
5.Hard
θ = 15°a

A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 15°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 20°a

A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 20°I = ½·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. Ek = 1858 kJ
  2. 2. IO = 0.6025 kg·m²
  3. 3. v = 7.073 m/s
  4. 4. P = 132.1 kW
  5. 5. μs = 0.07656
  6. 6. a = 2.237 m/s²

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