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
R = 0.55 mn = 300 rpm140 kg

A flywheel is a uniform solid disc of mass 140 kg and radius 0.55 m. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 140 kgR = 0.55 mn = 300 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 1.5 m1.7 m4.5 kg2 kg

A pendulum is made of a uniform slender rod (4.5 kg, 1.5 m long) pivoted at its top end O, with a thin solid disc of mass 2 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 1.5 mmdisc = 2 kgr = 0.2 md = 1.7 m
IO = kg·m²
3.Medium
ω = ?4 kgL = 0.9 mm = 3 kg

A uniform slender rod of mass 3 kg and length 0.9 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 = 3 kgL = 0.9 mmball = 4 kgg = 9.81 m/s²
ω = rad/s
4.Medium
n = 1900 rpmTb​ = 200 N·mI = 6 kg·m²

A flywheel with a moment of inertia of 6 kg·m² spins at 1900 rpm. A brake applies a constant friction torque of 200 N·m. How long t does it take to stop?

I = 6 kg·m²n = 1900 rpmTb = 200 N·m
t = s
5.Hard
disc: 32 kgring: 11 kgn1​ = 650 rpm

A uniform solid disc (mass 32 kg, radius 0.15 m) spins freely at 650 rpm about a vertical frictionless shaft. A thin ring of mass 11 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 = 32 kgMring = 11 kgR = 0.15 mn1 = 650 rpm
ΔE = J
6.Hard
θ = 10°a

A solid cylinder rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 10°I = ½·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. Ek = 10.45 kJ
  2. 2. IO = 9.195 kg·m²
  3. 3. ω = 4.897 rad/s
  4. 4. t = 5.969 s
  5. 5. ΔE = 339.8 J
  6. 6. μs = 0.05878

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