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 = 2.6 mGOd = 0.8 mm = 10 kg

A uniform slender rod of mass 10 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10 kgL = 2.6 md = 0.8 m
IO = kg·m²
2.Easy
Or = 0.1 mL = 0.8 m0.9 m5 kg7.5 kg

A pendulum is made of a uniform slender rod (5 kg, 0.8 m long) pivoted at its top end O, with a thin solid disc of mass 7.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.9 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 5 kgL = 0.8 mmdisc = 7.5 kgr = 0.1 md = 0.9 m
IO = kg·m²
3.Medium
v = ?2.5 kgL = 1.6 mm = 4 kg

A uniform slender rod of mass 4 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 kg is fixed to its free end. 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 = 1.6 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
4.Medium
n = 2700 rpmP = 148 kW

A shaft transmits 148 kW at 2700 rpm. Find the torque T in the shaft.

P = 148 kWn = 2700 rpm
T = N·m
5.Hard
θ = 20°a

A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 20°I = ½·m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 10°vs = 5 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 5 m along the slope.

θ = 10°s = 5 mI = ½·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s

Answer key

  1. 1. IO = 12.03 kg·m²
  2. 2. IO = 7.179 kg·m²
  3. 3. v = 6.071 m/s
  4. 4. T = 523.4 N·m
  5. 5. μs = 0.1213
  6. 6. ω = 11.23 rad/s

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