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 = 0.5 m0 → 1800 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1800 rpm. The driving torque is a constant 1800 N·m and friction can be ignored. How long t does this take?

m = 150 kgk = 0.5 mn1 = 0 rpmn2 = 1800 rpmT = 1800 N·m
t = s
2.Easy
k = 0.5 m0 → 1600 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1600 rpm. The driving torque is a constant 220 N·m and friction can be ignored. How long t does this take?

m = 150 kgk = 0.5 mn1 = 0 rpmn2 = 1600 rpmT = 220 N·m
t = s
3.Medium
n = 1400 rpmTb​ = 60 N·mI = 9 kg·m²

A flywheel with a moment of inertia of 9 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 60 N·m. How long t does it take to stop?

I = 9 kg·m²n = 1400 rpmTb = 60 N·m
t = s
4.Medium
n = 300 rpmTb​ = 90 N·mI = 22.5 kg·m²

A flywheel with a moment of inertia of 22.5 kg·m² spins at 300 rpm. A brake applies a constant friction torque of 90 N·m. How many revolutions N does the flywheel make before it stops?

I = 22.5 kg·m²n = 300 rpmTb = 90 N·m
N = rev
5.Hard
540 m/s25 g0.41 mL = 0.9 m9.5 kgφ

A uniform slender rod of mass 9.5 kg and length 0.9 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 540 m/s hits the rod 0.41 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 = 9.5 kgL = 0.9 mm = 25 gv = 540 m/sd = 0.41 mg = 9.81 m/s²
φ = °
6.Hard
100 m/s35 g0.69 mL = 1.6 m9 kg

A uniform slender rod of mass 9 kg and length 1.6 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 100 m/s hits the rod 0.69 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 9 kgL = 1.6 mm = 35 gv = 100 m/sd = 0.69 m
ω = rad/s

Answer key

  1. 1. t = 3.927 s
  2. 2. t = 28.56 s
  3. 3. t = 21.99 s
  4. 4. N = 19.63 rev
  5. 5. φ = 30.89 °
  6. 6. ω = 0.3138 rad/s

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