#Linear and Rotational Motion: A Last-Minute Review 🚀

Hey there, future AP Physics 1 master! Let's get these concepts locked down for your exam. Remember, linear and rotational motion aren't separate worlds—they're two sides of the same coin. We'll explore how they connect, making those tricky circular motion problems much easier. Let's dive in!

Rotational motion is a high-value topic on the AP exam. Expect to see it in both multiple-choice and free-response questions. Understanding the relationship between linear and angular quantities is crucial.

#🔗 Linking Linear and Rotational Motion

#Distance Traveled During Rotation

• Key Idea: When something rotates, points on that object travel a linear distance. This distance depends on how far the point is from the center and how much the object has rotated.

• Formula: $Delta s = rDelta\theta$ 📏

  • $Delta s$ is the linear distance traveled.
  • $r$ is the radius (distance from the axis of rotation).
  • $Delta\theta$ is the angle of rotation (in radians).

• Analogy: Imagine a point on a spinning bike wheel. As the wheel turns, the point moves along the edge. The distance it travels is the arc length, $\Delta s$.

• Example: If a point is 0.2 m from the center of a wheel and the wheel rotates by $\pi$ radians (180°), the point travels $\Delta s = (0.2 \text{ m})(\pi \text{ rad}) = 0.2\pi \text{ m}$.

#Linear vs. Angular Quantities

• Key Idea: Linear and angular quantities are related by the radius of rotation. These equations help us translate between the two.

• Formulas:

  • $s = r\theta$ (arc length)
  • $v = r\omega$ (linear velocity)
  • $a_t = r\alpha$ (tangential acceleration)
  • Where:
    • $s$ is the arc length (linear distance).
    • $v$ is the linear velocity.
    • $a_t$ is the tangential acceleration.
    • $\theta$ is the angular displacement (in radians).
    • $\omega$ is the angular velocity.
    • $\alpha$ is the angular acceleration.

• Analogy: Think of a...