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
R = 0.7 mn = 300 rpm240 kg

A flywheel is a uniform solid disc of mass 240 kg and radius 0.7 m. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 240 kgR = 0.7 mn = 300 rpm
Ek = kJ
2.Easy
Or = 0.2 mL = 0.4 m0.6 m0.5 kg4.5 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 4.5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.6 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.4 mmdisc = 4.5 kgr = 0.2 md = 0.6 m
IO = kg·m²
3.Medium
n = 2000 rpmTb​ = 135 N·mI = 9.5 kg·m²

A flywheel with a moment of inertia of 9.5 kg·m² spins at 2000 rpm. A brake applies a constant friction torque of 135 N·m. How long t does it take to stop?

I = 9.5 kg·m²n = 2000 rpmTb = 135 N·m
t = s
4.Medium
L = 2.7 mm = 8 kgα

A uniform slender rod of mass 8 kg and length 2.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 8 kgL = 2.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 25°vs = 7.5 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 7.5 m along the slope.

θ = 25°s = 7.5 mI = ½·m·r²g = 9.81 m/s²
v = m/s
6.Hard
disc: 30 kgring: 6 kgn1​ = 100 rpm

A uniform solid disc (mass 30 kg, radius 0.15 m) spins freely at 100 rpm about a vertical frictionless shaft. A thin ring of mass 6 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 30 kgMring = 6 kgR = 0.15 mn1 = 100 rpm
ΔE = J

Answer key

  1. 1. Ek = 29.02 kJ
  2. 2. IO = 1.737 kg·m²
  3. 3. t = 14.74 s
  4. 4. atip = 14.71 m/s²
  5. 5. v = 6.439 m/s
  6. 6. ΔE = 5.287 J

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