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
L = 3 mGOd = 0.7 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.7 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9.5 kgL = 3 md = 0.7 m
IO = kg·m²
2.Easy
L = 2.1 mGOd = 0.9 mm = 6 kg

A uniform slender rod of mass 6 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 0.9 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 6 kgL = 2.1 md = 0.9 m
IO = kg·m²
3.Medium
n = 1700 rpmTb​ = 80 N·mI = 29.5 kg·m²

A flywheel with a moment of inertia of 29.5 kg·m² spins at 1700 rpm. A brake applies a constant friction torque of 80 N·m. How long t does it take to stop?

I = 29.5 kg·m²n = 1700 rpmTb = 80 N·m
t = s
4.Medium
2.5 kgaαM = 7.5 kgR = 0.25 m

A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 0.5 m.

m = 2.5 kgM = 7.5 kgR = 0.25 mg = 9.81 m/s²h = 0.5 m
v = m/s
5.Hard
7.5 m/sω

A solid cylinder of mass 11.5 kg rolls without slipping at 7.5 m/s. Find its rotational kinetic energy Erot.

m = 11.5 kgv = 7.5 m/sI = ½·m·r²
Erot = J
6.Hard
0.8 m0.35 mn1​ = 45 rpm

A person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 2.5 kg·m² about the axis. They turn at 45 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 2.5 kg·m²m = 2 × 2 kgr1 = 0.8 mr2 = 0.35 mn1 = 45 rpm
n2 = rpm

Answer key

  1. 1. IO = 11.78 kg·m²
  2. 2. IO = 7.065 kg·m²
  3. 3. t = 65.65 s
  4. 4. v = 1.981 m/s
  5. 5. Erot = 161.7 J
  6. 6. n2 = 76.15 rpm

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