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 = 0.45 mn = 400 rpm240 kg

A flywheel is a uniform solid disc of mass 240 kg and radius 0.45 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 240 kgR = 0.45 mn = 400 rpm
Ek = kJ
2.Easy
L = 3 mGOd = 0.8 mm = 4 kg

A uniform slender rod of mass 4 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4 kgL = 3 md = 0.8 m
IO = kg·m²
3.Medium
n = 2700 rpmT = 1800 N·m

A motor delivers a torque of 1800 N·m at 2700 rpm. Find its power output P in kW.

T = 1800 N·mn = 2700 rpm
P = kW
4.Medium
n = 1200 rpmTb​ = 50 N·mI = 21 kg·m²

A flywheel with a moment of inertia of 21 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 50 N·m. How many revolutions N does the flywheel make before it stops?

I = 21 kg·m²n = 1200 rpmTb = 50 N·m
N = rev
5.Hard
θ = 25°vs = 6.5 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 6.5 m along the slope.

θ = 25°s = 6.5 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
3.5 m/sω

A thin hoop of mass 4.5 kg rolls without slipping at 3.5 m/s. Find its total kinetic energy Ek.

m = 4.5 kgv = 3.5 m/sI = m·r²
Ek = J

Answer key

  1. 1. Ek = 21.32 kJ
  2. 2. IO = 5.56 kg·m²
  3. 3. P = 508.9 kW
  4. 4. N = 527.8 rev
  5. 5. v = 5.994 m/s
  6. 6. Ek = 55.13 J

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