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 = 0.3 mn = 3000 rpm260 kg

A flywheel of mass 260 kg has a radius of gyration of 0.3 m about its axis. It spins at 3000 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgk = 0.3 mn = 3000 rpm
Ek = kJ
2.Easy
Or = 0.15 mL = 1 m1.15 m2.5 kg6.5 kg

A pendulum is made of a uniform slender rod (2.5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 6.5 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.15 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 1 mmdisc = 6.5 kgr = 0.15 md = 1.15 m
IO = kg·m²
3.Medium
L = 0.5 mm = 5 kgα

A uniform slender rod of mass 5 kg and length 0.5 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 = 5 kgL = 0.5 mg = 9.81 m/s²
R = N
4.Medium
n = 1200 rpmTb​ = 150 N·mI = 20 kg·m²

A flywheel with a moment of inertia of 20 kg·m² spins at 1200 rpm. A brake applies a constant friction torque of 150 N·m. How many revolutions N does the flywheel make before it stops?

I = 20 kg·m²n = 1200 rpmTb = 150 N·m
N = rev
5.Hard
100 m/s25 g1.01 mL = 1.4 m2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 100 m/s hits the rod 1.01 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 2.5 kgL = 1.4 mm = 25 gv = 100 m/sd = 1.01 m
ω = rad/s
6.Hard
disc: 40 kgring: 14 kgn1​ = 350 rpm

A uniform solid disc (mass 40 kg, radius 0.2 m) spins freely at 350 rpm about a vertical frictionless shaft. A thin ring of mass 14 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 40 kgMring = 14 kgR = 0.2 mn1 = 350 rpm
n2 = rpm

Answer key

  1. 1. Ek = 1155 kJ
  2. 2. IO = 9.503 kg·m²
  3. 3. R = 12.26 N
  4. 4. N = 167.6 rev
  5. 5. ω = 1.522 rad/s
  6. 6. n2 = 205.9 rpm

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