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 = 0.1 m0 → 200 rpm130 kg

A flywheel of mass 130 kg with a radius of gyration of 0.1 m is accelerated uniformly from rest to 200 rpm. This takes 19 s. Ignoring friction, find the constant torque T needed.

m = 130 kgk = 0.1 mn1 = 0 rpmn2 = 200 rpmt = 19 s
T = N·m
2.Easy
Or = 0.25 mL = 0.7 m0.95 m4.5 kg6 kg

A pendulum is made of a uniform slender rod (4.5 kg, 0.7 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.95 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 0.7 mmsphere = 6 kgr = 0.25 md = 0.95 m
IO = kg·m²
3.Medium
L = 2.2 mm = 17 kgα

A uniform slender rod of mass 17 kg and length 2.2 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 = 17 kgL = 2.2 mg = 9.81 m/s²
atip = m/s²
4.Medium
8.5 kgaαM = 4.5 kgR = 0.15 m

An 8.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 kg and radius 0.15 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 1 m.

m = 8.5 kgM = 4.5 kgR = 0.15 mg = 9.81 m/s²h = 1 m
v = m/s
5.Hard
disc: 23 kgring: 2 kgn1​ = 400 rpm

A uniform solid disc (mass 23 kg, radius 0.25 m) spins freely at 400 rpm about a vertical frictionless shaft. A thin ring of mass 2 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 = 23 kgMring = 2 kgR = 0.25 mn1 = 400 rpm
ΔE = J
6.Hard
6.5 m/sω

A thin hoop of mass 7.5 kg rolls without slipping at 6.5 m/s. Find its rotational kinetic energy Erot.

m = 7.5 kgv = 6.5 m/sI = m·r²
Erot = J

Answer key

  1. 1. T = 1.433 N·m
  2. 2. IO = 6.3 kg·m²
  3. 3. atip = 14.71 m/s²
  4. 4. v = 3.939 m/s
  5. 5. ΔE = 93.42 J
  6. 6. Erot = 158.4 J

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