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 = 2.5 mGOd = 0.3 mm = 12 kg

A uniform slender rod of mass 12 kg and length 2.5 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 12 kgL = 2.5 md = 0.3 m
IO = kg·m²
2.Easy
k = 0.2 m0 → 1000 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.2 m is accelerated uniformly from rest to 1000 rpm. This takes 4 s. Ignoring friction, find the constant torque T needed.

m = 10 kgk = 0.2 mn1 = 0 rpmn2 = 1000 rpmt = 4 s
T = N·m
3.Medium
n = 1600 rpmTb​ = 185 N·mI = 19 kg·m²

A flywheel with a moment of inertia of 19 kg·m² spins at 1600 rpm. A brake applies a constant friction torque of 185 N·m. How many revolutions N does the flywheel make before it stops?

I = 19 kg·m²n = 1600 rpmTb = 185 N·m
N = rev
4.Medium
ω = ?L = 1.8 mm = 3 kg

A uniform slender rod of mass 3 kg and length 1.8 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 = 3 kgL = 1.8 mg = 9.81 m/s²
ω = rad/s
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
θ = 10°vs = 6.5 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 6.5 m along the slope.

θ = 10°s = 6.5 mI = (2/3)·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. IO = 7.33 kg·m²
  2. 2. T = 10.47 N·m
  3. 3. N = 229.4 rev
  4. 4. ω = 4.044 rad/s
  5. 5. a = 2.764 m/s²
  6. 6. v = 3.645 m/s

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