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
L = 2.3 mGOd = 0.85 mm = 1.5 kg

A uniform slender rod of mass 1.5 kg and length 2.3 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1.5 kgL = 2.3 md = 0.85 m
IO = kg·m²
2.Easy
Or = 0.05 mL = 1.4 m1.45 m5 kg2 kg

A pendulum is made of a uniform slender rod (5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 2 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.45 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 5 kgL = 1.4 mmsphere = 2 kgr = 0.05 md = 1.45 m
IO = kg·m²
3.Medium
ω = ?2 kgL = 0.8 mm = 10 kg

A uniform slender rod of mass 10 kg and length 0.8 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 10 kgL = 0.8 mmball = 2 kgg = 9.81 m/s²
ω = rad/s
4.Medium
L = 2.2 mm = 12 kgα

A uniform slender rod of mass 12 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 vertical force R that the pin exerts on the rod just after release.

m = 12 kgL = 2.2 mg = 9.81 m/s²
R = N
5.Hard
0.65 m0.2 mn1​ = 35 rpm

A person stands on a frictionless turntable and holds a 3 kg dumbbell in each hand, 0.65 m from the axis. The person and turntable alone have a moment of inertia of 3.5 kg·m² about the axis. They turn at 35 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 3.5 kg·m²m = 2 × 3 kgr1 = 0.65 mr2 = 0.2 mn1 = 35 rpm
n2 = rpm
6.Hard
disc: 13 kgring: 16 kgn1​ = 100 rpm

A uniform solid disc (mass 13 kg, radius 0.45 m) spins freely at 100 rpm about a vertical frictionless shaft. A thin ring of mass 16 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 = 13 kgMring = 16 kgR = 0.45 mn1 = 100 rpm
ΔE = J

Answer key

  1. 1. IO = 1.745 kg·m²
  2. 2. IO = 7.474 kg·m²
  3. 3. ω = 5.674 rad/s
  4. 4. R = 29.43 N
  5. 5. n2 = 56.48 rpm
  6. 6. ΔE = 51.32 J

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