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
k = 0.4 m0 → 1400 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 1400 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.4 mn1 = 0 rpmn2 = 1400 rpmt = 28 s
T = N·m
2.Easy
L = 0.9 mGOd = 0.25 mm = 7 kg

A uniform slender rod of mass 7 kg and length 0.9 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7 kgL = 0.9 md = 0.25 m
IO = kg·m²
3.Medium
n = 2100 rpmTb​ = 145 N·mI = 11 kg·m²

A flywheel with a moment of inertia of 11 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 145 N·m. How many revolutions N does the flywheel make before it stops?

I = 11 kg·m²n = 2100 rpmTb = 145 N·m
N = rev
4.Medium
L = 0.5 mm = 7 kgα

A uniform slender rod of mass 7 kg and length 0.5 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 = 7 kgL = 0.5 mg = 9.81 m/s²
α = rad/s²
5.Hard
0.6 m0.25 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 4.5 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 = 4.5 kg·m²m = 2 × 5 kgr1 = 0.6 mr2 = 0.25 mn1 = 40 rpm
n2 = rpm
6.Hard
560 m/s45 g0.45 mL = 1 m6 kg

A uniform slender rod of mass 6 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 560 m/s hits the rod 0.45 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 6 kgL = 1 mm = 45 gv = 560 m/sd = 0.45 m
ω = rad/s

Answer key

  1. 1. T = 100.5 N·m
  2. 2. IO = 0.91 kg·m²
  3. 3. N = 292 rev
  4. 4. α = 29.43 rad/s²
  5. 5. n2 = 63.22 rpm
  6. 6. ω = 5.644 rad/s

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