Question 1 of 3 · Mass Moments & Rigid-Body Dynamics · Intermediate · About 22 min

Pendulum with a disk attached to a rod

A rigid pendulum consists of a uniform slender rod $1.50\,\mathrm{m}$ long of mass $2.0\,\mathrm{kg}$ , pinned at its top $O$ , and a solid circular disk of mass $3.0\,\mathrm{kg}$ and radius $0.25 m$ whose centre is fixed at the rod lower end. The disk plane and rod lie in the page. Determine the total mass moment of inertia about and the radius of gyration of the assembly about that axis.

A vertical pendulum. Pin O in a small support at the top. A slender straight rod hangs 1.50 m down from O to the centre G of a solid circular disk. The disk radius is 0.25 m, so the disk diameter is one third of the rod length. A thin radius line from G to the right edge of the disk. A vertical dimension beside the rod from O to G. Labels: O; G; 1.50 m; 0.25 m; rod: 2 kg; disk: 3 kg — Schematic, not to scale unless dimensions are given.

Given

Rod 1.50 m, 2 kg
Solid disk radius 0.25 m, mass 3 kg
Disk centre 1.50 m below pivot

Find

$I_O$
Radius of gyration $k_O$

Assumptions

All members and connections are idealised as specified in the question.
Use g = 9.81 m/s^2 where gravitational acceleration is required.

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Pendulum with a disk attached to a rod

Given

Find

Assumptions

Worked solution