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 = 0.5 m300 → 2200 rpm30 kg

A flywheel of mass 30 kg with a radius of gyration of 0.5 m is accelerated uniformly from 300 rpm to 2200 rpm. This takes 21 s. Ignoring friction, find the constant torque T needed.

m = 30 kgk = 0.5 mn1 = 300 rpmn2 = 2200 rpmt = 21 s
T = N·m
2.Easy
Or = 0.25 mL = 1.3 m1.55 m3.5 kg6.5 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 6.5 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.55 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1.3 mmdisc = 6.5 kgr = 0.25 md = 1.55 m
IO = kg·m²
3.Medium
n = 800 rpmTb​ = 30 N·mI = 13 kg·m²

A flywheel with a moment of inertia of 13 kg·m² spins at 800 rpm. A brake applies a constant friction torque of 30 N·m. How many revolutions N does the flywheel make before it stops?

I = 13 kg·m²n = 800 rpmTb = 30 N·m
N = rev
4.Medium
L = 2.3 mm = 2 kgα

A uniform slender rod of mass 2 kg and length 2.3 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 = 2 kgL = 2.3 mg = 9.81 m/s²
atip = m/s²
5.Hard
140 m/s5 g0.63 mL = 0.7 m3.5 kg

A uniform slender rod of mass 3.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 5 g bullet moving horizontally at 140 m/s hits the rod 0.63 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 3.5 kgL = 0.7 mm = 5 gv = 140 m/sd = 0.63 m
ω = rad/s
6.Hard
1.5 m/sω

A solid cylinder of mass 3.5 kg rolls without slipping at 1.5 m/s. Find its total kinetic energy Ek.

m = 3.5 kgv = 1.5 m/sI = ½·m·r²
Ek = J

Answer key

  1. 1. T = 71.06 N·m
  2. 2. IO = 17.79 kg·m²
  3. 3. N = 242 rev
  4. 4. atip = 14.71 m/s²
  5. 5. ω = 0.7688 rad/s
  6. 6. Ek = 5.906 J

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