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 = 1.3 mGOd = 0.3 mm = 10.5 kg

A uniform slender rod of mass 10.5 kg and length 1.3 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10.5 kgL = 1.3 md = 0.3 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.6 m0.8 m1 kg9 kg

A pendulum is made of a uniform slender rod (1 kg, 0.6 m long) pivoted at its top end O, with a solid sphere of mass 9 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 0.6 mmsphere = 9 kgr = 0.2 md = 0.8 m
IO = kg·m²
3.Medium
n = 2600 rpmT = 1590 N·m

A motor delivers a torque of 1590 N·m at 2600 rpm. Find its power output P in kW.

T = 1590 N·mn = 2600 rpm
P = kW
4.Medium
L = 0.9 mm = 12 kgα

A uniform slender rod of mass 12 kg and length 0.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 12 kgL = 0.9 mg = 9.81 m/s²
α = rad/s²
5.Hard
4.5 m/sω

A solid sphere of mass 12 kg rolls without slipping at 4.5 m/s. Find its rotational kinetic energy Erot.

m = 12 kgv = 4.5 m/sI = (2/5)·m·r²
Erot = J
6.Hard
0.7 m0.3 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 2.5 kgr1 = 0.7 mr2 = 0.3 mn1 = 25 rpm
n2 = rpm

Answer key

  1. 1. IO = 2.424 kg·m²
  2. 2. IO = 6.024 kg·m²
  3. 3. P = 432.9 kW
  4. 4. α = 16.35 rad/s²
  5. 5. Erot = 48.6 J
  6. 6. n2 = 50.64 rpm

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