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 = 0.5 mn = 3000 rpm90 kg

A flywheel is a uniform solid disc of mass 90 kg and radius 0.5 m. It spins at 3000 rpm. Find its kinetic energy Ek in kJ.

M = 90 kgR = 0.5 mn = 3000 rpm
Ek = kJ
2.Easy
L = 1.8 mGOd = 0.85 mm = 11 kg

A uniform slender rod of mass 11 kg and length 1.8 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11 kgL = 1.8 md = 0.85 m
IO = kg·m²
3.Medium
10.5 kgaαM = 5.5 kgR = 0.5 m

A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 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 3.5 m.

m = 10.5 kgM = 5.5 kgR = 0.5 mg = 9.81 m/s²h = 3.5 m
v = m/s
4.Medium
6.5 kgaαM = 18.5 kgR = 0.25 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 18.5 kg and radius 0.25 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 = 18.5 kgR = 0.25 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 15°vs = 10 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 10 m along the slope.

θ = 15°s = 10 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
0.8 m0.25 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 6 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 3.5 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3.5 kg·m²m = 2 × 6 kgr1 = 0.8 mr2 = 0.25 mn1 = 40 rpm
n2 = rpm

Answer key

  1. 1. Ek = 555.2 kJ
  2. 2. IO = 10.92 kg·m²
  3. 3. v = 7.377 m/s
  4. 4. α = 16.19 rad/s²
  5. 5. v = 5.818 m/s
  6. 6. n2 = 105.2 rpm

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