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
k = 0.4 mn = 1100 rpm100 kg

A flywheel of mass 100 kg has a radius of gyration of 0.4 m about its axis. It spins at 1100 rpm. Find its kinetic energy Ek in kJ.

M = 100 kgk = 0.4 mn = 1100 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.5 m0.7 m2 kg7.5 kg

A pendulum is made of a uniform slender rod (2 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 7.5 kg and radius 0.2 m fixed to its lower end. The centre of the sphere is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2 kgL = 0.5 mmsphere = 7.5 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
ω = ?4.5 kgL = 1.8 mm = 3 kg

A uniform slender rod of mass 3 kg and length 1.8 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 3 kgL = 1.8 mmball = 4.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
v = ?L = 2 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 2 m is pinned at one end and released from rest in a horizontal position. 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 = 9.5 kgL = 2 mg = 9.81 m/s²
v = m/s
5.Hard
8.5 m/sω

A hollow sphere of mass 16.5 kg rolls without slipping at 8.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 16.5 kgv = 8.5 m/sI = (2/3)·m·r²
p = %
6.Hard
320 m/s45 g1 mL = 1 m6 kg

A uniform slender rod of mass 6 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 320 m/s hits the rod 1 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 6 kgL = 1 mm = 45 gv = 320 m/sd = 1 m
ω = rad/s

Answer key

  1. 1. Ek = 106.2 kJ
  2. 2. IO = 3.962 kg·m²
  3. 3. ω = 3.448 rad/s
  4. 4. v = 7.672 m/s
  5. 5. p = 40 %
  6. 6. ω = 7.042 rad/s

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