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
Or = 0.25 mL = 1.1 m1.35 m4.5 kg9 kg

A pendulum is made of a uniform slender rod (4.5 kg, 1.1 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 1.1 mmdisc = 9 kgr = 0.25 md = 1.35 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.9 m1.1 m1.5 kg8 kg

A pendulum is made of a uniform slender rod (1.5 kg, 0.9 m long) pivoted at its top end O, with a thin solid disc of mass 8 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1.5 kgL = 0.9 mmdisc = 8 kgr = 0.2 md = 1.1 m
IO = kg·m²
3.Medium
n = 2400 rpmTb​ = 60 N·mI = 21.5 kg·m²

A flywheel with a moment of inertia of 21.5 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?

I = 21.5 kg·m²n = 2400 rpmTb = 60 N·m
t = s
4.Medium
ω = ?2 kgL = 1.9 mm = 10 kg

A uniform slender rod of mass 10 kg and length 1.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 10 kgL = 1.9 mmball = 2 kgg = 9.81 m/s²
ω = rad/s
5.Hard
9 m/sω

A hollow sphere of mass 19 kg rolls without slipping at 9 m/s. Find its total kinetic energy Ek.

m = 19 kgv = 9 m/sI = (2/3)·m·r²
Ek = J
6.Hard
440 m/s35 g0.63 mL = 1.2 m1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 440 m/s hits the rod 0.63 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1.5 kgL = 1.2 mm = 35 gv = 440 m/sd = 0.63 m
ω = rad/s

Answer key

  1. 1. IO = 18.5 kg·m²
  2. 2. IO = 10.25 kg·m²
  3. 3. t = 90.06 s
  4. 4. ω = 3.681 rad/s
  5. 5. Ek = 1283 J
  6. 6. ω = 13.22 rad/s

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