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
L = 1.6 mGOd = 0.45 mm = 1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.6 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1.5 kgL = 1.6 md = 0.45 m
IO = kg·m²
2.Easy
Or = 0.15 mL = 0.5 m0.65 m0.5 kg6.5 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 6.5 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 0.65 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.5 mmsphere = 6.5 kgr = 0.15 md = 0.65 m
IO = kg·m²
3.Medium
n = 400 rpmT = 810 N·m

A motor delivers a torque of 810 N·m at 400 rpm. Find its power output P in kW.

T = 810 N·mn = 400 rpm
P = kW
4.Medium
0.5 kgaαM = 8.5 kgR = 0.2 m

A 0.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8.5 kg and radius 0.2 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 = 0.5 kgM = 8.5 kgR = 0.2 mg = 9.81 m/s²h = 3.5 m
v = m/s
5.Hard
6 m/sω

A thin hoop of mass 5.5 kg rolls without slipping at 6 m/s. Find its total kinetic energy Ek.

m = 5.5 kgv = 6 m/sI = m·r²
Ek = J
6.Hard
360 m/s30 g0.92 mL = 1.3 m7 kg

A uniform slender rod of mass 7 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 360 m/s hits the rod 0.92 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 7 kgL = 1.3 mm = 30 gv = 360 m/sd = 0.92 m
ω = rad/s

Answer key

  1. 1. IO = 0.6238 kg·m²
  2. 2. IO = 2.846 kg·m²
  3. 3. P = 33.93 kW
  4. 4. v = 2.689 m/s
  5. 5. Ek = 198 J
  6. 6. ω = 2.504 rad/s

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