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 mGOd = 0.35 mm = 1 kg

A uniform slender rod of mass 1 kg and length 1 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 = 1 kgL = 1 md = 0.35 m
IO = kg·m²
2.Easy
k = 0.1 m600 → 1200 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.1 m is accelerated uniformly from 600 rpm to 1200 rpm. The driving torque is a constant 13 N·m and friction can be ignored. How long t does this take?

m = 40 kgk = 0.1 mn1 = 600 rpmn2 = 1200 rpmT = 13 N·m
t = s
3.Medium
L = 2 mm = 4 kgα

A uniform slender rod of mass 4 kg and length 2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 4 kgL = 2 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 1000 rpmTb​ = 140 N·mI = 19 kg·m²

A flywheel with a moment of inertia of 19 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 140 N·m. How long t does it take to stop?

I = 19 kg·m²n = 1000 rpmTb = 140 N·m
t = s
5.Hard
disc: 37 kgring: 6 kgn1​ = 100 rpm

A uniform solid disc (mass 37 kg, radius 0.2 m) spins freely at 100 rpm about a vertical frictionless shaft. A thin ring of mass 6 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 = 37 kgMring = 6 kgR = 0.2 mn1 = 100 rpm
ΔE = J
6.Hard
260 m/s10 g0.98 mL = 1.7 m1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.7 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 260 m/s hits the rod 0.98 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 1.5 kgL = 1.7 mm = 10 gv = 260 m/sd = 0.98 m
ω = rad/s

Answer key

  1. 1. IO = 0.2058 kg·m²
  2. 2. t = 1.933 s
  3. 3. α = 7.357 rad/s²
  4. 4. t = 14.21 s
  5. 5. ΔE = 9.937 J
  6. 6. ω = 1.752 rad/s

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