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 = 0.2 mn = 400 rpm200 kg

A flywheel of mass 200 kg has a radius of gyration of 0.2 m about its axis. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 200 kgk = 0.2 mn = 400 rpm
Ek = kJ
2.Easy
R = 0.3 mn = 400 rpm300 kg

A flywheel is a uniform solid disc of mass 300 kg and radius 0.3 m. It spins at 400 rpm. Find its kinetic energy Ek in kJ.

M = 300 kgR = 0.3 mn = 400 rpm
Ek = kJ
3.Medium
n = 1600 rpmTb​ = 55 N·mI = 2 kg·m²

A flywheel with a moment of inertia of 2 kg·m² spins at 1600 rpm. A brake applies a constant friction torque of 55 N·m. How many revolutions N does the flywheel make before it stops?

I = 2 kg·m²n = 1600 rpmTb = 55 N·m
N = rev
4.Medium
v = ?2.5 kgL = 0.9 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 4.5 kgL = 0.9 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
5.Hard
θ = 10°as = 8.5 m

A solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 8.5 m down the slope?

θ = 10°I = (2/5)·m·r²g = 9.81 m/s²s = 8.5 m
t = s
6.Hard
360 m/s45 g0.76 mL = 1.4 m6 kgφ

A uniform slender rod of mass 6 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 360 m/s hits the rod 0.76 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 = 6 kgL = 1.4 mm = 45 gv = 360 m/sd = 0.76 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. Ek = 7.018 kJ
  2. 2. Ek = 11.84 kJ
  3. 3. N = 81.24 rev
  4. 4. v = 4.579 m/s
  5. 5. t = 3.738 s
  6. 6. φ = 57.48 °

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