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 = 0.55 m0 → 1700 rpm70 kg

A flywheel of mass 70 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 1700 rpm. The driving torque is a constant 180 N·m and friction can be ignored. How long t does this take?

m = 70 kgk = 0.55 mn1 = 0 rpmn2 = 1700 rpmT = 180 N·m
t = s
2.Easy
k = 0.45 mn = 800 rpm210 kg

A flywheel of mass 210 kg has a radius of gyration of 0.45 m about its axis. It spins at 800 rpm. Find its kinetic energy Ek in kJ.

M = 210 kgk = 0.45 mn = 800 rpm
Ek = kJ
3.Medium
n = 1100 rpmTb​ = 175 N·mI = 13 kg·m²

A flywheel with a moment of inertia of 13 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 175 N·m. How many revolutions N does the flywheel make before it stops?

I = 13 kg·m²n = 1100 rpmTb = 175 N·m
N = rev
4.Medium
n = 3000 rpmTb​ = 180 N·mI = 19 kg·m²

A flywheel with a moment of inertia of 19 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 180 N·m. How long t does it take to stop?

I = 19 kg·m²n = 3000 rpmTb = 180 N·m
t = s
5.Hard
120 m/s30 g1.13 mL = 1.2 m5 kgφ

A uniform slender rod of mass 5 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 120 m/s hits the rod 1.13 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 kgL = 1.2 mm = 30 gv = 120 m/sd = 1.13 mg = 9.81 m/s²
φ = °
6.Hard
θ = 30°as = 6 m

A solid cylinder rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 6 m down the slope?

θ = 30°I = ½·m·r²g = 9.81 m/s²s = 6 m
t = s

Answer key

  1. 1. t = 20.94 s
  2. 2. Ek = 149.2 kJ
  3. 3. N = 78.44 rev
  4. 4. t = 33.16 s
  5. 5. φ = 27.63 °
  6. 6. t = 1.916 s

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