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 = 1.1 mGOd = 0.45 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 1.1 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 = 7.5 kgL = 1.1 md = 0.45 m
IO = kg·m²
2.Easy
k = 0.6 m400 → 2200 rpm190 kg

A flywheel of mass 190 kg with a radius of gyration of 0.6 m is accelerated uniformly from 400 rpm to 2200 rpm. This takes 22 s. Ignoring friction, find the constant torque T needed.

m = 190 kgk = 0.6 mn1 = 400 rpmn2 = 2200 rpmt = 22 s
T = N·m
3.Medium
ω = ?4.5 kgL = 1.5 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 1.5 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 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 = 6.5 kgL = 1.5 mmball = 4.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
n = 1000 rpmT = 1670 N·m

A motor delivers a torque of 1670 N·m at 1000 rpm. Find its power output P in kW.

T = 1670 N·mn = 1000 rpm
P = kW
5.Hard
θ = 15°a

A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 15°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
8.5 m/sω

A solid cylinder of mass 19.5 kg rolls without slipping at 8.5 m/s. Find its total kinetic energy Ek.

m = 19.5 kgv = 8.5 m/sI = ½·m·r²
Ek = J

Answer key

  1. 1. IO = 2.275 kg·m²
  2. 2. T = 586 N·m
  3. 3. ω = 3.899 rad/s
  4. 4. P = 174.9 kW
  5. 5. μs = 0.07656
  6. 6. Ek = 1057 J

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