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
k = 0.6 mn = 2900 rpm230 kg

A flywheel of mass 230 kg has a radius of gyration of 0.6 m about its axis. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 230 kgk = 0.6 mn = 2900 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.5 m0.7 m1 kg7.5 kg

A pendulum is made of a uniform slender rod (1 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 7.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1 kgL = 0.5 mmdisc = 7.5 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
n = 2900 rpmTb​ = 35 N·mI = 38.5 kg·m²

A flywheel with a moment of inertia of 38.5 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 35 N·m. How many revolutions N does the flywheel make before it stops?

I = 38.5 kg·m²n = 2900 rpmTb = 35 N·m
N = rev
4.Medium
n = 1000 rpmTb​ = 85 N·mI = 18.5 kg·m²

A flywheel with a moment of inertia of 18.5 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 85 N·m. How many revolutions N does the flywheel make before it stops?

I = 18.5 kg·m²n = 1000 rpmTb = 85 N·m
N = rev
5.Hard
520 m/s20 g0.48 mL = 0.7 m5.5 kgφ

A uniform slender rod of mass 5.5 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 520 m/s hits the rod 0.48 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 5.5 kgL = 0.7 mm = 20 gv = 520 m/sd = 0.48 mg = 9.81 m/s²
φ = °
6.Hard
600 m/s35 g0.29 mL = 0.6 m8 kg

A uniform slender rod of mass 8 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 600 m/s hits the rod 0.29 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 8 kgL = 0.6 mm = 35 gv = 600 m/sd = 0.29 m
ω = rad/s

Answer key

  1. 1. Ek = 3818 kJ
  2. 2. IO = 3.908 kg·m²
  3. 3. N = 8073 rev
  4. 4. N = 189.9 rev
  5. 5. φ = 74.16 °
  6. 6. ω = 6.324 rad/s

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