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 = 0.2 mn = 2400 rpm80 kg

A flywheel is a uniform solid disc of mass 80 kg and radius 0.2 m. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 80 kgR = 0.2 mn = 2400 rpm
Ek = kJ
2.Easy
L = 1.8 mGOd = 0.6 mm = 6 kg

A uniform slender rod of mass 6 kg and length 1.8 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 = 6 kgL = 1.8 md = 0.6 m
IO = kg·m²
3.Medium
8 kgaαM = 4.5 kgR = 0.25 m

An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 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 1 m.

m = 8 kgM = 4.5 kgR = 0.25 mg = 9.81 m/s²h = 1 m
v = m/s
4.Medium
v = ?2 kgL = 1.6 mm = 8 kg

A uniform slender rod of mass 8 kg and length 1.6 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 speed v of the free end as the rod swings through the vertical position.

m = 8 kgL = 1.6 mmball = 2 kgg = 9.81 m/s²
v = m/s
5.Hard
θ = 35°vs = 5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 5 m along the slope.

θ = 35°s = 5 mI = m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s
6.Hard
6 m/sω

A solid cylinder of mass 9 kg rolls without slipping at 6 m/s. Find its total kinetic energy Ek.

m = 9 kgv = 6 m/sI = ½·m·r²
Ek = J

Answer key

  1. 1. Ek = 50.53 kJ
  2. 2. IO = 3.78 kg·m²
  3. 3. v = 3.913 m/s
  4. 4. v = 6.353 m/s
  5. 5. ω = 21.22 rad/s
  6. 6. Ek = 243 J

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