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 = 0.9 mGOd = 0.4 mm = 10 kg

A uniform slender rod of mass 10 kg and length 0.9 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10 kgL = 0.9 md = 0.4 m
IO = kg·m²
2.Easy
Or = 0.1 mL = 1 m1.1 m2 kg9 kg

A pendulum is made of a uniform slender rod (2 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 1.1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2 kgL = 1 mmdisc = 9 kgr = 0.1 md = 1.1 m
IO = kg·m²
3.Medium
n = 1100 rpmP = 143 kW

A shaft transmits 143 kW at 1100 rpm. Find the torque T in the shaft.

P = 143 kWn = 1100 rpm
T = N·m
4.Medium
n = 1500 rpmTb​ = 185 N·mI = 4.5 kg·m²

A flywheel with a moment of inertia of 4.5 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 185 N·m. How long t does it take to stop?

I = 4.5 kg·m²n = 1500 rpmTb = 185 N·m
t = s
5.Hard
θ = 10°as = 5.5 m

A thin hoop rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 5.5 m down the slope?

θ = 10°I = m·r²g = 9.81 m/s²s = 5.5 m
t = s
6.Hard
0.6 m0.25 mn1​ = 60 rpm

A person stands on a frictionless turntable and holds a 3.5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 60 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 3.5 kgr1 = 0.6 mr2 = 0.25 mn1 = 60 rpm
n2 = rpm

Answer key

  1. 1. IO = 2.275 kg·m²
  2. 2. IO = 11.6 kg·m²
  3. 3. T = 1241 N·m
  4. 4. t = 3.821 s
  5. 5. t = 3.594 s
  6. 6. n2 = 82.98 rpm

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