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 = 0.5 mGOd = 0.15 mm = 11 kg

A uniform slender rod of mass 11 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11 kgL = 0.5 md = 0.15 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.5 m0.7 m4 kg4 kg

A pendulum is made of a uniform slender rod (4 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 4 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 0.5 mmdisc = 4 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
n = 2500 rpmP = 192.5 kW

A shaft transmits 192.5 kW at 2500 rpm. Find the torque T in the shaft.

P = 192.5 kWn = 2500 rpm
T = N·m
4.Medium
n = 2000 rpmTb​ = 195 N·mI = 2 kg·m²

A flywheel with a moment of inertia of 2 kg·m² spins at 2000 rpm. A brake applies a constant friction torque of 195 N·m. How many revolutions N does the flywheel make before it stops?

I = 2 kg·m²n = 2000 rpmTb = 195 N·m
N = rev
5.Hard
θ = 10°vs = 7 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7 m along the slope.

θ = 10°s = 7 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 35°vs = 9 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 9 m along the slope.

θ = 35°s = 9 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s

Answer key

  1. 1. IO = 0.4767 kg·m²
  2. 2. IO = 2.373 kg·m²
  3. 3. T = 735.3 N·m
  4. 4. N = 35.8 rev
  5. 5. v = 3.783 m/s
  6. 6. ω = 31.18 rad/s

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