Topic: Theory of Machines / Vibrations
Polar moment in inertia $(I_{p})$ of a circular disc is to be determined by suspending it by a wire and noting the frequency of oscillations (f).
- A. $I_{p} \propto \frac{1}{f^{2}}$
- B. $I_{p} \propto f^{2}$
- C. $I_{p} \propto f$
- D. $I_{p} \propto \frac{1}{f}$
Answer: A. $I_{p} \propto \frac{1}{f^{2}}$
Explanation: Radius of gyration $k \propto \frac{1}{f_{n}}$. Since polar moment of inertia $I = mk^{2}$, we have $I \propto \frac{1}{f_{n}^{2}}$.