#AP Physics C: Mechanics - Circular Motion 🎢

Hey! Let's get you prepped for circular motion. This is a key area, and we'll break it down so it feels like a breeze. Remember, you've got this! 💪

#Motion in Circular Paths

#Centripetal Acceleration

• Definition: Centripetal acceleration is the acceleration that keeps an object moving in a circle. It's always directed towards the center of the circle, constantly changing the direction of the velocity, not the speed. Think of it as the force that pulls you inward when you're spinning around. 🔄

• Magnitude: The magnitude of centripetal acceleration ($a_c$) can be calculated using the formula:

  $$a_{c} = \frac{v^2}{r}$$

  where:

  • $v$ is the tangential speed (how fast the object is moving along the circle)
  • $r$ is the radius of the circular path

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

#Forces Causing Centripetal Acceleration

• Origin: Centripetal acceleration is caused by a net force that always points towards the center of the circle. This force can be:

  • A single force
  • Multiple forces
  • Components of forces

• Vertical Loops (e.g., Rollercoasters):

  • At the top of a loop, the minimum speed required to stay on the track is when gravity alone provides the centripetal force. 🎢

  • The minimum speed ($v$) can be calculated using:

    $$v = \sqrt{gr}$$

    where:

    • $g$ is the acceleration due to gravity (approximately 9.8 m/s²)
    • $r$ is the radius of the loop

• Banked Surfaces (e.g., Racetrack Turns):

  • Here, both the normal force and static friction work together to provide the necessary centripetal force. ...