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 = 0.35 mn = 2900 rpm200 kg

A flywheel of mass 200 kg has a radius of gyration of 0.35 m about its axis. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 200 kgk = 0.35 mn = 2900 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.5 m0.7 m5 kg3.5 kg

A pendulum is made of a uniform slender rod (5 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 3.5 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 = 5 kgL = 0.5 mmdisc = 3.5 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
n = 2300 rpmTb​ = 190 N·mI = 34.5 kg·m²

A flywheel with a moment of inertia of 34.5 kg·m² spins at 2300 rpm. A brake applies a constant friction torque of 190 N·m. How long t does it take to stop?

I = 34.5 kg·m²n = 2300 rpmTb = 190 N·m
t = s
4.Medium
L = 2.8 mm = 10.5 kgα

A uniform slender rod of mass 10.5 kg and length 2.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 10.5 kgL = 2.8 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 35°as = 3.5 m

A solid sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 3.5 m down the slope?

θ = 35°I = (2/5)·m·r²g = 9.81 m/s²s = 3.5 m
t = s
6.Hard
θ = 25°vs = 3 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find its speed v after it has rolled 3 m along the slope.

θ = 25°s = 3 mI = ½·m·r²g = 9.81 m/s²
v = m/s

Answer key

  1. 1. Ek = 1130 kJ
  2. 2. IO = 2.202 kg·m²
  3. 3. t = 43.73 s
  4. 4. α = 5.255 rad/s²
  5. 5. t = 1.32 s
  6. 6. v = 4.072 m/s

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