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 = 0.4 mGOd = 0.15 mm = 5 kg

A uniform slender rod of mass 5 kg and length 0.4 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 = 5 kgL = 0.4 md = 0.15 m
IO = kg·m²
2.Easy
Or = 0.1 mL = 0.7 m0.8 m4 kg9.5 kg

A pendulum is made of a uniform slender rod (4 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 9.5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 0.8 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4 kgL = 0.7 mmsphere = 9.5 kgr = 0.1 md = 0.8 m
IO = kg·m²
3.Medium
n = 2600 rpmTb​ = 15 N·mI = 18.5 kg·m²

A flywheel with a moment of inertia of 18.5 kg·m² spins at 2600 rpm. A brake applies a constant friction torque of 15 N·m. How many revolutions N does the flywheel make before it stops?

I = 18.5 kg·m²n = 2600 rpmTb = 15 N·m
N = rev
4.Medium
ω = ?5 kgL = 1.2 mm = 10 kg

A uniform slender rod of mass 10 kg and length 1.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 10 kgL = 1.2 mmball = 5 kgg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 40°vs = 7 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 7 m along the slope.

θ = 40°s = 7 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 35°a

A hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 35°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 0.1792 kg·m²
  2. 2. IO = 6.771 kg·m²
  3. 3. N = 7276 rev
  4. 4. ω = 4.429 rad/s
  5. 5. v = 7.672 m/s
  6. 6. a = 3.376 m/s²

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