Circular and Rotational Kinematics

Define angular position, velocity, and acceleration, and derive their relationships using calculus.

Prove the formula for centripetal acceleration (a_c = v^2/r) using geometric or vector methods.

For non-uniform circular motion, derive the tangential and centripetal acceleration components from first principles.

Prove the relationships between linear and angular kinematic quantities (v = ωr, a_t = αr).

Solve problems involving time-varying angular velocity and acceleration using integration.

Apply the 3D vector forms of angular velocity (ω) and acceleration (α) to solve problems in spatial circular motion.