#AP Physics 1: Circular Motion & Kepler's Laws 🚀

Hey there, future physicist! Let's get you prepped for the AP exam with a super-focused review of circular motion and Kepler's laws. We'll break down the concepts, highlight key formulas, and get you feeling confident. Let's dive in!

#Circular Motion: The Basics

#Centripetal Acceleration 🎡

• Definition: Acceleration directed towards the center of a circular path. It's what keeps objects moving in a circle, constantly changing their direction.

• Formula: $$a_{c} = \frac{v^{2}}{r}$$ where:

  • $a_c$ is centripetal acceleration
  • $v$ is tangential speed
  • $r$ is the radius of the circular path

• Direction: Always points towards the center of the circle, perpendicular to the object's velocity.

• Cause: Can be caused by various forces (or components of forces), like tension, friction, or gravity.

*Caption: Centripetal acceleration (ac) is always directed toward the center of the circle, while the velocity (v) is tangential to the circle.*

• Vertical Loops: At the top of a loop, the minimum speed to maintain circular motion is when gravity provides the entire centripetal force: $$v = \sqrt{gr}$$. Think roller coasters!

• Banked Curves: Static friction and normal forces combine to create the centripetal force on banked turns (like race tracks). Remember, we only analyze these quantitatively when friction isn't needed for uniform circular motion.

• Conical Pendulums: Tension in the string has a component that contributes to the centripetal force (think amusement park swings).

#Forces in Circular Motion

• Forces cause centripetal acceleration. The net force always points to the center of the circle.

• Examples include tension in a string, gravity for orbiting bodies, and friction for a car turning.

#Tangential Acceleration

• Definition: Acceleration along the circular path that changes an object's speed.

• Effect: ...