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
R = 0.4 mn = 2800 rpm70 kg

A flywheel is a uniform solid disc of mass 70 kg and radius 0.4 m. It spins at 2800 rpm. Find its kinetic energy Ek in kJ.

M = 70 kgR = 0.4 mn = 2800 rpm
Ek = kJ
2.Easy
R = 0.25 mn = 1100 rpm260 kg

A flywheel is a uniform solid disc of mass 260 kg and radius 0.25 m. It spins at 1100 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgR = 0.25 mn = 1100 rpm
Ek = kJ
3.Medium
ω = ?L = 1.2 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 1.2 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 = 9.5 kgL = 1.2 mg = 9.81 m/s²
ω = rad/s
4.Medium
n = 700 rpmTb​ = 175 N·mI = 18 kg·m²

A flywheel with a moment of inertia of 18 kg·m² spins at 700 rpm. A brake applies a constant friction torque of 175 N·m. How many revolutions N does the flywheel make before it stops?

I = 18 kg·m²n = 700 rpmTb = 175 N·m
N = rev
5.Hard
θ = 40°as = 3 m

A solid cylinder rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 3 m down the slope?

θ = 40°I = ½·m·r²g = 9.81 m/s²s = 3 m
t = s
6.Hard
440 m/s25 g1.27 mL = 1.3 m9.5 kg

A uniform slender rod of mass 9.5 kg and length 1.3 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 440 m/s hits the rod 1.27 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 9.5 kgL = 1.3 mm = 25 gv = 440 m/sd = 1.27 m
ω = rad/s

Answer key

  1. 1. Ek = 240.7 kJ
  2. 2. Ek = 53.91 kJ
  3. 3. ω = 4.952 rad/s
  4. 4. N = 43.98 rev
  5. 5. t = 1.195 s
  6. 6. ω = 2.591 rad/s

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