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 = 1.7 mGOd = 0.7 mm = 8 kg

A uniform slender rod of mass 8 kg and length 1.7 m rotates about an axis O perpendicular to the rod, 0.7 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 8 kgL = 1.7 md = 0.7 m
IO = kg·m²
2.Easy
Or = 0.25 mL = 1.2 m1.45 m1 kg4.5 kg

A pendulum is made of a uniform slender rod (1 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 1.2 mmsphere = 4.5 kgr = 0.25 md = 1.45 m
IO = kg·m²
3.Medium
L = 1.4 mm = 15.5 kgα

A uniform slender rod of mass 15.5 kg and length 1.4 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 15.5 kgL = 1.4 mg = 9.81 m/s²
R = N
4.Medium
L = 3 mm = 10 kgα

A uniform slender rod of mass 10 kg and length 3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 10 kgL = 3 mg = 9.81 m/s²
atip = m/s²
5.Hard
5.5 m/sω

A thin hoop of mass 19.5 kg rolls without slipping at 5.5 m/s. Find its rotational kinetic energy Erot.

m = 19.5 kgv = 5.5 m/sI = m·r²
Erot = J
6.Hard
θ = 25°a

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 25°I = m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 5.847 kg·m²
  2. 2. IO = 10.05 kg·m²
  3. 3. R = 38.01 N
  4. 4. atip = 14.71 m/s²
  5. 5. Erot = 294.9 J
  6. 6. μs = 0.2332

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