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 = 0.6 mn = 600 rpm110 kg

A flywheel is a uniform solid disc of mass 110 kg and radius 0.6 m. It spins at 600 rpm. Find its kinetic energy Ek in kJ.

M = 110 kgR = 0.6 mn = 600 rpm
Ek = kJ
2.Easy
Or = 0.15 mL = 1.3 m1.45 m5 kg3.5 kg

A pendulum is made of a uniform slender rod (5 kg, 1.3 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 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 = 5 kgL = 1.3 mmdisc = 3.5 kgr = 0.15 md = 1.45 m
IO = kg·m²
3.Medium
6.5 kgaαM = 10 kgR = 0.35 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10 kg and radius 0.35 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 6.5 kgM = 10 kgR = 0.35 mg = 9.81 m/s²
α = rad/s²
4.Medium
12 kgaαM = 17 kgR = 0.5 m

A 12 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17 kg and radius 0.5 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 0.5 m.

m = 12 kgM = 17 kgR = 0.5 mg = 9.81 m/s²h = 0.5 m
v = m/s
5.Hard
0.75 m0.35 mn1​ = 30 rpm

A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.75 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 30 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 5.5 kgr1 = 0.75 mr2 = 0.35 mn1 = 30 rpm
n2 = rpm
6.Hard
disc: 29 kgring: 13 kgn1​ = 300 rpm

A uniform solid disc (mass 29 kg, radius 0.3 m) spins freely at 300 rpm about a vertical frictionless shaft. A thin ring of mass 13 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 = 29 kgMring = 13 kgR = 0.3 mn1 = 300 rpm
ΔE = J

Answer key

  1. 1. Ek = 39.08 kJ
  2. 2. IO = 10.21 kg·m²
  3. 3. α = 15.84 rad/s²
  4. 4. v = 2.396 m/s
  5. 5. n2 = 52.88 rpm
  6. 6. ΔE = 304.4 J

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