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 = 2.2 mGOd = 0.5 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 2.2 m rotates about an axis O perpendicular to the rod, 0.5 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 2.5 kgL = 2.2 md = 0.5 m
IO = kg·m²
2.Easy
L = 2.6 mGOd = 0.4 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, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10 kgL = 2.6 md = 0.4 m
IO = kg·m²
3.Medium
ω = ?L = 0.5 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. 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 = 2.5 kgL = 0.5 mg = 9.81 m/s²
ω = rad/s
4.Medium
ω = ?L = 2.4 mm = 2 kg

A uniform slender rod of mass 2 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. 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 = 2 kgL = 2.4 mg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 10°vs = 2 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 2 m along the slope.

θ = 10°s = 2 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s
6.Hard
θ = 25°a

A thin hoop 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 = m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 1.633 kg·m²
  2. 2. IO = 7.233 kg·m²
  3. 3. ω = 7.672 rad/s
  4. 4. ω = 3.502 rad/s
  5. 5. v = 2.022 m/s
  6. 6. a = 2.073 m/s²

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