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 = 2.7 mGOd = 0.3 mm = 10.5 kg

A uniform slender rod of mass 10.5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10.5 kgL = 2.7 md = 0.3 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.4 m0.6 m4 kg4.5 kg

A pendulum is made of a uniform slender rod (4 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 4.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 0.4 mmdisc = 4.5 kgr = 0.2 md = 0.6 m
IO = kg·m²
3.Medium
n = 1000 rpmTb​ = 65 N·mI = 6 kg·m²

A flywheel with a moment of inertia of 6 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 65 N·m. How long t does it take to stop?

I = 6 kg·m²n = 1000 rpmTb = 65 N·m
t = s
4.Medium
L = 2.5 mm = 12.5 kgα

A uniform slender rod of mass 12.5 kg and length 2.5 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 = 12.5 kgL = 2.5 mg = 9.81 m/s²
R = N
5.Hard
480 m/s10 g0.24 mL = 0.6 m4 kgφ

A uniform slender rod of mass 4 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 480 m/s hits the rod 0.24 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 = 0.6 mm = 10 gv = 480 m/sd = 0.24 mg = 9.81 m/s²
φ = °
6.Hard
θ = 35°a

A thin hoop rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 35°I = m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 7.324 kg·m²
  2. 2. IO = 1.923 kg·m²
  3. 3. t = 9.666 s
  4. 4. R = 30.66 N
  5. 5. φ = 28 °
  6. 6. μs = 0.3501

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