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 = 2.4 mGOd = 0.6 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 2.4 m rotates about an axis O perpendicular to the rod, 0.6 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9.5 kgL = 2.4 md = 0.6 m
IO = kg·m²
2.Easy
R = 0.3 mn = 700 rpm30 kg

A flywheel is a uniform solid disc of mass 30 kg and radius 0.3 m. It spins at 700 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgR = 0.3 mn = 700 rpm
Ek = kJ
3.Medium
L = 1.9 mm = 3.5 kgα

A uniform slender rod of mass 3.5 kg and length 1.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 3.5 kgL = 1.9 mg = 9.81 m/s²
atip = m/s²
4.Medium
n = 2300 rpmTb​ = 120 N·mI = 26.5 kg·m²

A flywheel with a moment of inertia of 26.5 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 120 N·m. How many revolutions N does the flywheel make before it stops?

I = 26.5 kg·m²n = 2300 rpmTb = 120 N·m
N = rev
5.Hard
0.9 m0.3 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.9 m from the axis. The person and turntable alone have a moment of inertia of 3 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3 kg·m²m = 2 × 2.5 kgr1 = 0.9 mr2 = 0.3 mn1 = 25 rpm
n2 = rpm
6.Hard
240 m/s25 g0.29 mL = 0.6 m8.5 kgφ

A uniform slender rod of mass 8.5 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 240 m/s hits the rod 0.29 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 8.5 kgL = 0.6 mm = 25 gv = 240 m/sd = 0.29 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. IO = 7.98 kg·m²
  2. 2. Ek = 3.627 kJ
  3. 3. atip = 14.71 m/s²
  4. 4. N = 1019 rev
  5. 5. n2 = 51.09 rpm
  6. 6. φ = 19.79 °

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