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
Or = 0.15 mL = 1.3 m1.45 m1.5 kg8.5 kg

A pendulum is made of a uniform slender rod (1.5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 8.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1.5 kgL = 1.3 mmdisc = 8.5 kgr = 0.15 md = 1.45 m
IO = kg·m²
2.Easy
k = 0.55 m0 → 1900 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 1900 rpm. This takes 11 s. Ignoring friction, find the constant torque T needed.

m = 40 kgk = 0.55 mn1 = 0 rpmn2 = 1900 rpmt = 11 s
T = N·m
3.Medium
ω = ?4.5 kgL = 2 mm = 8 kg

A uniform slender rod of mass 8 kg and length 2 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 = 8 kgL = 2 mmball = 4.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
n = 1800 rpmTb​ = 95 N·mI = 16 kg·m²

A flywheel with a moment of inertia of 16 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 95 N·m. How many revolutions N does the flywheel make before it stops?

I = 16 kg·m²n = 1800 rpmTb = 95 N·m
N = rev
5.Hard
disc: 10 kgring: 9 kgn1​ = 1000 rpm

A uniform solid disc (mass 10 kg, radius 0.5 m) spins freely at 1000 rpm about a vertical frictionless shaft. A thin ring of mass 9 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 10 kgMring = 9 kgR = 0.5 mn1 = 1000 rpm
ΔE = J
6.Hard
3 m/sω

A solid sphere of mass 18.5 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 18.5 kgv = 3 m/sI = (2/5)·m·r²
p = %

Answer key

  1. 1. IO = 18.81 kg·m²
  2. 2. T = 218.9 N·m
  3. 3. ω = 3.411 rad/s
  4. 4. N = 476.2 rev
  5. 5. ΔE = 4406 J
  6. 6. p = 28.57 %

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