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 = 1.7 mGOd = 0.5 mm = 2 kg

A uniform slender rod of mass 2 kg and length 1.7 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 = 2 kgL = 1.7 md = 0.5 m
IO = kg·m²
2.Easy
Or = 0.05 mL = 1.2 m1.25 m4 kg10 kg

A pendulum is made of a uniform slender rod (4 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 1.2 mmsphere = 10 kgr = 0.05 md = 1.25 m
IO = kg·m²
3.Medium
n = 1100 rpmP = 109 kW

A shaft transmits 109 kW at 1100 rpm. Find the torque T in the shaft.

P = 109 kWn = 1100 rpm
T = N·m
4.Medium
n = 2500 rpmTb​ = 170 N·mI = 34.5 kg·m²

A flywheel with a moment of inertia of 34.5 kg·m² spins at 2500 rpm. A brake applies a constant friction torque of 170 N·m. How long t does it take to stop?

I = 34.5 kg·m²n = 2500 rpmTb = 170 N·m
t = s
5.Hard
2.5 m/sω

A hollow sphere of mass 16.5 kg rolls without slipping at 2.5 m/s. Find its rotational kinetic energy Erot.

m = 16.5 kgv = 2.5 m/sI = (2/3)·m·r²
Erot = J
6.Hard
0.9 m0.35 mn1​ = 55 rpm

A person stands on a frictionless turntable and holds a 2 kg dumbbell in each hand, 0.9 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 55 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 = 1.5 kg·m²m = 2 × 2 kgr1 = 0.9 mr2 = 0.35 mn1 = 55 rpm
n2 = rpm

Answer key

  1. 1. IO = 0.9817 kg·m²
  2. 2. IO = 17.55 kg·m²
  3. 3. T = 946.2 N·m
  4. 4. t = 53.13 s
  5. 5. Erot = 34.38 J
  6. 6. n2 = 131 rpm

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