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 mGOd = 0.25 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 1 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5.5 kgL = 1 md = 0.25 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.8 m1 m1.5 kg7 kg

A pendulum is made of a uniform slender rod (1.5 kg, 0.8 m long) pivoted at its top end O, with a thin solid disc of mass 7 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 1 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1.5 kgL = 0.8 mmdisc = 7 kgr = 0.2 md = 1 m
IO = kg·m²
3.Medium
L = 1.7 mm = 1 kgα

A uniform slender rod of mass 1 kg and length 1.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 1 kgL = 1.7 mg = 9.81 m/s²
R = N
4.Medium
2 kgaαM = 8.5 kgR = 0.1 m

A 2 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8.5 kg and radius 0.1 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 2 kgM = 8.5 kgR = 0.1 mg = 9.81 m/s²
a = m/s²
5.Hard
θ = 25°a

A solid cylinder rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 25°I = ½·m·r²g = 9.81 m/s²
a = m/s²
6.Hard
440 m/s10 g0.87 mL = 1.8 m9 kg

A uniform slender rod of mass 9 kg and length 1.8 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 440 m/s hits the rod 0.87 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 9 kgL = 1.8 mm = 10 gv = 440 m/sd = 0.87 m
ω = rad/s

Answer key

  1. 1. IO = 0.8021 kg·m²
  2. 2. IO = 7.46 kg·m²
  3. 3. R = 2.453 N
  4. 4. a = 3.139 m/s²
  5. 5. a = 2.764 m/s²
  6. 6. ω = 0.3935 rad/s

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