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.

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1.Easy
L = 0.9 mGOd = 0.4 mm = 3 kg

A uniform slender rod of mass 3 kg and length 0.9 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 0.9 md = 0.4 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.9 m1.1 m2 kg1.5 kg

A pendulum is made of a uniform slender rod (2 kg, 0.9 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2 kgL = 0.9 mmsphere = 1.5 kgr = 0.2 md = 1.1 m
IO = kg·m²
3.Medium
n = 900 rpmTb​ = 50 N·mI = 9.5 kg·m²

A flywheel with a moment of inertia of 9.5 kg·m² spins at 900 rpm. A brake applies a constant friction torque of 50 N·m. How long t does it take to stop?

I = 9.5 kg·m²n = 900 rpmTb = 50 N·m
t = s
4.Medium
n = 2700 rpmP = 46 kW

A shaft transmits 46 kW at 2700 rpm. Find the torque T in the shaft.

P = 46 kWn = 2700 rpm
T = N·m
5.Hard
0.9 m0.15 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 4.5 kg dumbbell in each hand, 0.9 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 4 kg·m²m = 2 × 4.5 kgr1 = 0.9 mr2 = 0.15 mn1 = 40 rpm
n2 = rpm
6.Hard
8.5 m/sω

A hollow sphere of mass 18 kg rolls without slipping at 8.5 m/s. Find its total kinetic energy Ek.

m = 18 kgv = 8.5 m/sI = (2/3)·m·r²
Ek = J

Answer key

  1. 1. IO = 0.6825 kg·m²
  2. 2. IO = 2.379 kg·m²
  3. 3. t = 17.91 s
  4. 4. T = 162.7 N·m
  5. 5. n2 = 107.5 rpm
  6. 6. Ek = 1084 J

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