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 = 1.2 mGOd = 0.35 mm = 11 kg

A uniform slender rod of mass 11 kg and length 1.2 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11 kgL = 1.2 md = 0.35 m
IO = kg·m²
2.Easy
k = 0.55 m0 → 1400 rpm110 kg

A flywheel of mass 110 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 1400 rpm. The driving torque is a constant 170 N·m and friction can be ignored. How long t does this take?

m = 110 kgk = 0.55 mn1 = 0 rpmn2 = 1400 rpmT = 170 N·m
t = s
3.Medium
6.5 kgaαM = 10.5 kgR = 0.25 m

A 6.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 6.5 kgM = 10.5 kgR = 0.25 mg = 9.81 m/s²
α = rad/s²
4.Medium
v = ?1.5 kgL = 2.3 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 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 = 7.5 kgL = 2.3 mmball = 1.5 kgg = 9.81 m/s²
v = m/s
5.Hard
6.5 m/sω

A hollow sphere of mass 7.5 kg rolls without slipping at 6.5 m/s. Find its total kinetic energy Ek.

m = 7.5 kgv = 6.5 m/sI = (2/3)·m·r²
Ek = J
6.Hard
160 m/s15 g0.53 mL = 1.2 m3 kg

A uniform slender rod of mass 3 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 160 m/s hits the rod 0.53 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 3 kgL = 1.2 mm = 15 gv = 160 m/sd = 0.53 m
ω = rad/s

Answer key

  1. 1. IO = 2.667 kg·m²
  2. 2. t = 28.7 s
  3. 3. α = 21.71 rad/s²
  4. 4. v = 7.696 m/s
  5. 5. Ek = 264.1 J
  6. 6. ω = 0.8808 rad/s

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