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 = 0.8 mGOd = 0.3 mm = 3.5 kg

A uniform slender rod of mass 3.5 kg and length 0.8 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3.5 kgL = 0.8 md = 0.3 m
IO = kg·m²
2.Easy
Or = 0.15 mL = 1 m1.15 m3.5 kg9 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1 m long) pivoted at its top end O, with a thin solid disc of mass 9 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 1.15 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1 mmdisc = 9 kgr = 0.15 md = 1.15 m
IO = kg·m²
3.Medium
v = ?L = 0.5 mm = 2 kg

A uniform slender rod of mass 2 kg and length 0.5 m is pinned at one end and released from rest in a horizontal position. 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 = 0.5 mg = 9.81 m/s²
v = m/s
4.Medium
L = 0.8 mm = 1.5 kgα

A uniform slender rod of mass 1.5 kg and length 0.8 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 = 1.5 kgL = 0.8 mg = 9.81 m/s²
R = N
5.Hard
0.6 m0.25 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 3 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 3 kgr1 = 0.6 mr2 = 0.25 mn1 = 40 rpm
n2 = rpm
6.Hard
360 m/s40 g0.64 mL = 1.1 m4 kg

A uniform slender rod of mass 4 kg and length 1.1 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 360 m/s hits the rod 0.64 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 4 kgL = 1.1 mm = 40 gv = 360 m/sd = 0.64 m
ω = rad/s

Answer key

  1. 1. IO = 0.5017 kg·m²
  2. 2. IO = 13.17 kg·m²
  3. 3. v = 3.836 m/s
  4. 4. R = 3.679 N
  5. 5. n2 = 53.28 rpm
  6. 6. ω = 5.655 rad/s

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