#AP Physics C: Mechanics - Linear and Rotational Motion 🔄

Hey there, future physics master! Let's get you prepped for the exam with a super-focused review of linear and rotational motion. We'll make sure you're not just memorizing formulas, but truly understanding how everything connects. Let's dive in!

#Connecting Linear and Rotational Motion

This section is all about how linear motion (like moving in a straight line) and rotational motion (like spinning) are related. It’s like discovering the secret language that connects two seemingly different worlds of motion. Think of it as translating between two dialects of physics! 💡

#Key Relationships

• Displacement: Linear distance ($s$) is related to angular displacement ($\theta$) by: $s = r\theta$. This is your go-to for translating between how far something spins and how far it moves along a circle.
• Velocity: Linear velocity ($v$) is related to angular velocity ($\omega$) by: $v = r\omega$. This links how fast something spins to how fast it moves along a circle.
• Acceleration: Tangential acceleration ($a_T$) is related to angular acceleration ($\alpha$) by: $a_T = r\alpha$. This connects how quickly something's spin changes to how quickly its linear speed changes along the circle.

#Linear Motion of a Rotating Point

Let's zoom in on a single point as it rotates. This helps us understand how linear motion arises from circular motion.

#Linear Distance and Angle

• Concept: When a point rotates around a fixed axis, the linear distance it travels is directly proportional to the angle it sweeps out. Think of a point on a spinning wheel – the bigger the angle, the further it travels along the circle.
• Formula: $\Delta s = r \Delta \theta$ where:
  • $\Delta s$ is the linear distance traveled
  • $r$ is the radius
  • $\Delta \theta$ is the angular displacement (in radians)
• Analogy: Imagine a point on the edge of a spinn...