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 = 0.25 mn = 700 rpm30 kg

A flywheel of mass 30 kg has a radius of gyration of 0.25 m about its axis. It spins at 700 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgk = 0.25 mn = 700 rpm
Ek = kJ
2.Easy
L = 1.6 mGOd = 0.75 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 1.6 m rotates about an axis O perpendicular to the rod, 0.75 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7.5 kgL = 1.6 md = 0.75 m
IO = kg·m²
3.Medium
v = ?2.5 kgL = 1.9 mm = 8.5 kg

A uniform slender rod of mass 8.5 kg and length 1.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 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 = 8.5 kgL = 1.9 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
4.Medium
ω = ?4 kgL = 1.6 mm = 9 kg

A uniform slender rod of mass 9 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 = 9 kgL = 1.6 mmball = 4 kgg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 35°vs = 1.5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 1.5 m along the slope.

θ = 35°s = 1.5 mI = m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s
6.Hard
disc: 13 kgring: 6 kgn1​ = 450 rpm

A uniform solid disc (mass 13 kg, radius 0.35 m) spins freely at 450 rpm about a vertical frictionless shaft. A thin ring of mass 6 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 = 13 kgMring = 6 kgR = 0.35 mn1 = 450 rpm
n2 = rpm

Answer key

  1. 1. Ek = 5.038 kJ
  2. 2. IO = 5.819 kg·m²
  3. 3. v = 6.869 m/s
  4. 4. ω = 3.859 rad/s
  5. 5. ω = 9.684 rad/s
  6. 6. n2 = 234 rpm

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