Engineers use concepts from rotational dynamics and torque when they design machines. They apply simple rules to make machines work better and use energy more efficiently.

1. Calculating Torque: Torque ($\tau$) is found using this formula:
   $\tau = r \times F$
   Here, $r$ is the radius, and $F$ is the force being applied.

2. Rotational Equilibrium: Engineers make sure machines stay balanced by checking the total torque around a point called a pivot. This is shown as:
   $\sum \tau = 0$

3. Moment of Inertia: The moment of inertia ($I$) tells us how much an object resists changing its spinning motion. You can calculate it with the formula:
   $I = \sum m r^2$
   In this formula, $m$ is the mass, and $r$ is how far it is from the spinning point.

By using these ideas, engineers can create parts like gears and flywheels. These parts help improve how machines work and keep them stable.