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 = 0.55 mn = 2400 rpm60 kg

A flywheel of mass 60 kg has a radius of gyration of 0.55 m about its axis. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 60 kgk = 0.55 mn = 2400 rpm
Ek = kJ
2.Easy
Or = 0.15 mL = 1 m1.15 m4.5 kg2 kg

A pendulum is made of a uniform slender rod (4.5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 2 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 = 4.5 kgL = 1 mmdisc = 2 kgr = 0.15 md = 1.15 m
IO = kg·m²
3.Medium
13 kgaαM = 13 kgR = 0.45 m

A 13 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 13 kg and radius 0.45 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 = 13 kgM = 13 kgR = 0.45 mg = 9.81 m/s²
α = rad/s²
4.Medium
L = 0.6 mm = 20 kgα

A uniform slender rod of mass 20 kg and length 0.6 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 = 20 kgL = 0.6 mg = 9.81 m/s²
R = N
5.Hard
240 m/s50 g0.81 mL = 1.4 m4 kgφ

A uniform slender rod of mass 4 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 50 g bullet moving horizontally at 240 m/s hits the rod 0.81 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 4 kgL = 1.4 mm = 50 gv = 240 m/sd = 0.81 mg = 9.81 m/s²
φ = °
6.Hard
θ = 30°vs = 7.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 7.5 m along the slope.

θ = 30°s = 7.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. Ek = 573.2 kJ
  2. 2. IO = 4.167 kg·m²
  3. 3. α = 14.53 rad/s²
  4. 4. R = 49.05 N
  5. 5. φ = 68.94 °
  6. 6. ω = 29 rad/s

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