Physics

Physics

Problem

A solid metal disc has a moment of inertia I=2.0×10−4 kg m2I = 2.0 \times 10^{-4}\,\text{kg}\,\text{m}^2 about its central axis. (a) Convert this value into CGS units (g cm2\text{g}\,\text{cm}^2). Show every step of your working, including all unit conversions used. (b) Convert your CGS result back to SI units and verify that you recover the original value, thereby confirming the consistency of your conversion.
Intuitive explanation

The key to unit conversion is breaking it into prime factors: kg→g\text{kg} \to \text{g} (multiply by 1000) and m2→cm2\text{m}^2 \to \text{cm}^2 (multiply by 10410^4, since 1 m = 100 cm). Once you've converted forward systematically, reversing those same steps backward is a powerful way to catch errors and build confidence in your method—it's like solving an equation and plugging the answer back in.

Intuitive explanation

The key to unit conversion is breaking it into prime factors: kg→g\text{kg} \to \text{g} (multiply by 1000) and m2→cm2\text{m}^2 \to \text{cm}^2 (multiply by 10410^4, since 1 m = 100 cm). Once you've converted forward systematically, reversing those same steps backward is a powerful way to catch errors and build confidence in your method—it's like solving an equation and plugging the answer back in.

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