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 = 0.7 mn = 300 rpm120 kg

A flywheel is a uniform solid disc of mass 120 kg and radius 0.7 m. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 120 kgR = 0.7 mn = 300 rpm
Ek = kJ
2.Easy
Or = 0.25 mL = 0.8 m1.05 m3.5 kg9 kg

A pendulum is made of a uniform slender rod (3.5 kg, 0.8 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.25 m fixed to its lower end. The disc swings in its own plane and its centre is 1.05 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 0.8 mmdisc = 9 kgr = 0.25 md = 1.05 m
IO = kg·m²
3.Medium
0 → 2200 rpmI = 11 kg·m²

A motor brings a flywheel with a moment of inertia of 11 kg·m² from rest up to 2200 rpm in 28 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 11 kg·m²n = 2200 rpmt = 28 s
Pavg = kW
4.Medium
n = 2400 rpmTb​ = 120 N·mI = 5 kg·m²

A flywheel with a moment of inertia of 5 kg·m² spins at 2400 rpm. A brake applies a constant friction torque of 120 N·m. How many revolutions N does the flywheel make before it stops?

I = 5 kg·m²n = 2400 rpmTb = 120 N·m
N = rev
5.Hard
580 m/s45 g1.45 mL = 1.5 m4 kg

A uniform slender rod of mass 4 kg and length 1.5 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 580 m/s hits the rod 1.45 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 4 kgL = 1.5 mm = 45 gv = 580 m/sd = 1.45 m
ω = rad/s
6.Hard
8.5 m/sω

A thin hoop of mass 12 kg rolls without slipping at 8.5 m/s. Find its rotational kinetic energy Erot.

m = 12 kgv = 8.5 m/sI = m·r²
Erot = J

Answer key

  1. 1. Ek = 14.51 kJ
  2. 2. IO = 10.95 kg·m²
  3. 3. Pavg = 10.43 kW
  4. 4. N = 209.4 rev
  5. 5. ω = 12.23 rad/s
  6. 6. Erot = 433.5 J

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