#AP Physics C: Mechanics - Work & Energy in Rotational Motion 🚀

Hey there! Let's get you prepped for the exam with a super-focused review of rotational work and energy. We'll break down the concepts, highlight key points, and make sure you're feeling confident and ready to ace this section!

#1. Work Done by Torque

#1.1 Energy Transfer by Torque

• Torque, a rotational force, can transfer energy to or from an object when applied over an angular displacement. Think of it like pushing a door open 🚪—you're applying torque, and the door gains energy.

• The direction of the torque relative to the angular displacement determines whether energy is added to or removed from the system. Clockwise torque with clockwise displacement adds energy; clockwise torque with counterclockwise displacement removes energy.

• Example: Applying a clockwise torque to a door handle while opening the door transfers energy into the door, causing it to rotate.

#1.2 Work-Torque Relationship

• The work done on a rigid system by a torque depends on the magnitude of the torque and the angular displacement the system rotates through while the torque is applied.

• Calculating work involves integrating the torque with respect to the angular displacement over the interval of interest.

• Equation: $$W=\int_{\theta_{1}}^{\theta_{2}} \tau d \theta$$

  • $W$ represents the work done by the torque.
  • $\tau$ represents the magnitude of the torque as a function of angular position.
  • $\theta_{1}$ and $\theta_{2}$ represent the initial and final angular positions, respecti...