Q.Write down the difference between simple harmonic motion and angular simple harmonic motion.

Step 1. Displacement. In linear SHM, displacement is measured as a linear vector $\vec r$; in angular SHM, displacement is measured as an angular vector $\vec\theta$ (also called the angle of twist).

Step 2. Acceleration. Linear SHM has acceleration $\vec a=-\omega^2\vec r$; angular SHM has angular acceleration $\vec\alpha=-\omega^2\vec\theta$.

Step 3. Governing law. Linear SHM follows $\vec F=m\vec a$, where $m$ is the mass of the particle; angular SHM follows $\vec\tau=I\vec\alpha$, where $I$ is the moment of inertia of the body.

Step 4. Restoring law. Linear SHM's restoring force is $\vec F=-k\vec r$, with $k$ the force (spring) constant; angular SHM's restoring torque is $\vec\tau=-\kappa\vec\theta$, with $\kappa$ the restoring torsion constant (a property of the torsion fibre or suspension). …

Present the five-row correspondence: displacement, acceleration, governing law, restoring law, and angular fre …

• Mixing up which quantity is the 'inertia factor' in each case (mass for linear, moment of inertia for angular). …