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 = 0.2 mn = 700 rpm260 kg

A flywheel is a uniform solid disc of mass 260 kg and radius 0.2 m. It spins at 700 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgR = 0.2 mn = 700 rpm
Ek = kJ
2.Easy
Or = 0.25 mL = 1.1 m1.35 m2 kg1 kg

A pendulum is made of a uniform slender rod (2 kg, 1.1 m long) pivoted at its top end O, with a solid sphere of mass 1 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2 kgL = 1.1 mmsphere = 1 kgr = 0.25 md = 1.35 m
IO = kg·m²
3.Medium
0 → 300 rpmI = 22.5 kg·m²

A motor brings a flywheel with a moment of inertia of 22.5 kg·m² from rest up to 300 rpm in 7 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 22.5 kg·m²n = 300 rpmt = 7 s
Pavg = kW
4.Medium
v = ?4 kgL = 2.4 mm = 2 kg

A uniform slender rod of mass 2 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 = 2 kgL = 2.4 mmball = 4 kgg = 9.81 m/s²
v = m/s
5.Hard
2 m/sω

A hollow sphere of mass 0.5 kg rolls without slipping at 2 m/s. Find its total kinetic energy Ek.

m = 0.5 kgv = 2 m/sI = (2/3)·m·r²
Ek = J
6.Hard
0.7 m0.3 mn1​ = 50 rpm

A person stands on a frictionless turntable and holds a 1 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 50 rpm, then pull the dumbbells in to 0.3 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 1 kgr1 = 0.7 mr2 = 0.3 mn1 = 50 rpm
n2 = rpm

Answer key

  1. 1. Ek = 13.97 kJ
  2. 2. IO = 2.654 kg·m²
  3. 3. Pavg = 1.586 kW
  4. 4. v = 7.103 m/s
  5. 5. Ek = 1.667 J
  6. 6. n2 = 57.72 rpm

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