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
k = 0.35 mn = 1600 rpm280 kg

A flywheel of mass 280 kg has a radius of gyration of 0.35 m about its axis. It spins at 1600 rpm. Find its kinetic energy Ek in kJ.

M = 280 kgk = 0.35 mn = 1600 rpm
Ek = kJ
2.Easy
k = 0.3 mn = 600 rpm160 kg

A flywheel of mass 160 kg has a radius of gyration of 0.3 m about its axis. It spins at 600 rpm. Find its kinetic energy Ek in kJ.

M = 160 kgk = 0.3 mn = 600 rpm
Ek = kJ
3.Medium
v = ?0.5 kgL = 2.3 mm = 6 kg

A uniform slender rod of mass 6 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 0.5 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 = 6 kgL = 2.3 mmball = 0.5 kgg = 9.81 m/s²
v = m/s
4.Medium
0 → 900 rpmI = 25 kg·m²

A motor brings a flywheel with a moment of inertia of 25 kg·m² from rest up to 900 rpm in 8 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 25 kg·m²n = 900 rpmt = 8 s
Pavg = kW
5.Hard
0.9 m0.35 mn1​ = 45 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 4.5 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 = 4.5 kg·m²m = 2 × 2.5 kgr1 = 0.9 mr2 = 0.35 mn1 = 45 rpm
n2 = rpm
6.Hard
θ = 35°a

A solid cylinder rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 35°I = ½·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. Ek = 481.5 kJ
  2. 2. Ek = 28.42 kJ
  3. 3. v = 7.948 m/s
  4. 4. Pavg = 13.88 kW
  5. 5. n2 = 75.26 rpm
  6. 6. a = 3.751 m/s²

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