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 = 3 mGOd = 0.3 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 3 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 = 2.5 kgL = 3 md = 0.3 m
IO = kg·m²
2.Easy
L = 2.2 mGOd = 0.55 mm = 5 kg

A uniform slender rod of mass 5 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 2.2 md = 0.55 m
IO = kg·m²
3.Medium
n = 1300 rpmP = 130 kW

A shaft transmits 130 kW at 1300 rpm. Find the torque T in the shaft.

P = 130 kWn = 1300 rpm
T = N·m
4.Medium
n = 2900 rpmTb​ = 155 N·mI = 33 kg·m²

A flywheel with a moment of inertia of 33 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 155 N·m. How many revolutions N does the flywheel make before it stops?

I = 33 kg·m²n = 2900 rpmTb = 155 N·m
N = rev
5.Hard
0.8 m0.35 mn1​ = 20 rpm

A person stands on a frictionless turntable and holds a 5.5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 4 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 4 kg·m²m = 2 × 5.5 kgr1 = 0.8 mr2 = 0.35 mn1 = 20 rpm
n2 = rpm
6.Hard
0.85 m0.15 mn1​ = 60 rpm

A person stands on a frictionless turntable and holds a 1.5 kg dumbbell in each hand, 0.85 m from the axis. The person and turntable alone have a moment of inertia of 2.5 kg·m² about the axis. They turn at 60 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 = 2.5 kg·m²m = 2 × 1.5 kgr1 = 0.85 mr2 = 0.15 mn1 = 60 rpm
n2 = rpm

Answer key

  1. 1. IO = 2.1 kg·m²
  2. 2. IO = 3.529 kg·m²
  3. 3. T = 954.9 N·m
  4. 4. N = 1563 rev
  5. 5. n2 = 41.29 rpm
  6. 6. n2 = 109.1 rpm

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