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 = 1.5 mGOd = 0.5 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 1.5 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5.5 kgL = 1.5 md = 0.5 m
IO = kg·m²
2.Easy
R = 0.5 mn = 1600 rpm30 kg

A flywheel is a uniform solid disc of mass 30 kg and radius 0.5 m. It spins at 1600 rpm. Find its kinetic energy Ek in kJ.

M = 30 kgR = 0.5 mn = 1600 rpm
Ek = kJ
3.Medium
n = 2300 rpmTb​ = 85 N·mI = 22 kg·m²

A flywheel with a moment of inertia of 22 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 85 N·m. How many revolutions N does the flywheel make before it stops?

I = 22 kg·m²n = 2300 rpmTb = 85 N·m
N = rev
4.Medium
v = ?L = 1.4 mm = 4 kg

A uniform slender rod of mass 4 kg and length 1.4 m is pinned at one end and released from rest in a horizontal position. 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 kgL = 1.4 mg = 9.81 m/s²
v = m/s
5.Hard
0.85 m0.2 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 2.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 2.5 kgr1 = 0.85 mr2 = 0.2 mn1 = 40 rpm
n2 = rpm
6.Hard
disc: 21 kgring: 19 kgn1​ = 1000 rpm

A uniform solid disc (mass 21 kg, radius 0.35 m) spins freely at 1000 rpm about a vertical frictionless shaft. A thin ring of mass 19 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 21 kgMring = 19 kgR = 0.35 mn1 = 1000 rpm
n2 = rpm

Answer key

  1. 1. IO = 2.406 kg·m²
  2. 2. Ek = 52.64 kJ
  3. 3. N = 1195 rev
  4. 4. v = 6.419 m/s
  5. 5. n2 = 120.3 rpm
  6. 6. n2 = 355.9 rpm

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