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 = 0.35 mn = 1900 rpm270 kg

A flywheel of mass 270 kg has a radius of gyration of 0.35 m about its axis. It spins at 1900 rpm. Find its kinetic energy Ek in kJ.

M = 270 kgk = 0.35 mn = 1900 rpm
Ek = kJ
2.Easy
L = 1.7 mGOd = 0.25 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.7 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 2.5 kgL = 1.7 md = 0.25 m
IO = kg·m²
3.Medium
v = ?3 kgL = 2.1 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 2.1 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 4.5 kgL = 2.1 mmball = 3 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 1300 rpmTb​ = 30 N·mI = 15.5 kg·m²

A flywheel with a moment of inertia of 15.5 kg·m² spins at 1300 rpm. A brake applies a constant friction torque of 30 N·m. How many revolutions N does the flywheel make before it stops?

I = 15.5 kg·m²n = 1300 rpmTb = 30 N·m
N = rev
5.Hard
0.9 m0.15 mn1​ = 50 rpm

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.9 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 50 rpm, then pull the dumbbells in to 0.15 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3.5 kg·m²m = 2 × 1 kgr1 = 0.9 mr2 = 0.15 mn1 = 50 rpm
n2 = rpm
6.Hard
3 m/sω

A thin hoop of mass 4.5 kg rolls without slipping at 3 m/s. Find its total kinetic energy Ek.

m = 4.5 kgv = 3 m/sI = m·r²
Ek = J

Answer key

  1. 1. Ek = 654.7 kJ
  2. 2. IO = 0.7583 kg·m²
  3. 3. v = 6.933 m/s
  4. 4. N = 762 rev
  5. 5. n2 = 72.21 rpm
  6. 6. Ek = 40.5 J

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