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 = 0.1 m0 → 700 rpm50 kg

A flywheel of mass 50 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 700 rpm. The driving torque is a constant 12 N·m and friction can be ignored. How long t does this take?

m = 50 kgk = 0.1 mn1 = 0 rpmn2 = 700 rpmT = 12 N·m
t = s
2.Easy
Or = 0.05 mL = 1.2 m1.25 m4 kg3.5 kg

A pendulum is made of a uniform slender rod (4 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 3.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 1.2 mmsphere = 3.5 kgr = 0.05 md = 1.25 m
IO = kg·m²
3.Medium
v = ?3.5 kgL = 1.5 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3.5 kg is fixed to its free end. 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 = 2.5 kgL = 1.5 mmball = 3.5 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 1300 rpmTb​ = 175 N·mI = 32.5 kg·m²

A flywheel with a moment of inertia of 32.5 kg·m² spins at 1300 rpm. A brake applies a constant friction torque of 175 N·m. How long t does it take to stop?

I = 32.5 kg·m²n = 1300 rpmTb = 175 N·m
t = s
5.Hard
3 m/sω

A hollow sphere of mass 2 kg rolls without slipping at 3 m/s. Find its total kinetic energy Ek.

m = 2 kgv = 3 m/sI = (2/3)·m·r²
Ek = J
6.Hard
300 m/s25 g1.41 mL = 1.9 m9.5 kgφ

A uniform slender rod of mass 9.5 kg and length 1.9 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 300 m/s hits the rod 1.41 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 9.5 kgL = 1.9 mm = 25 gv = 300 m/sd = 1.41 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. t = 3.054 s
  2. 2. IO = 7.392 kg·m²
  3. 3. v = 5.68 m/s
  4. 4. t = 25.28 s
  5. 5. Ek = 15 J
  6. 6. φ = 19.05 °

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