When the speed changes along a circular path, two acceleration components exist simultaneously:

Centripetal (radial): $a_c$ = $v^2$/r (toward centre, always present) Tangential: $a_t$ = $\frac{dv}{dt}$ = d|v|/dt (along the tangent, only when speed changes)

Net acceleration: $a_{net}$ = sqrt($a_c^2$ + $a_t^2$) Angle with radius: phi = arctan$\frac{a_t}{a_c}$

Key point: The net force is NOT directed toward the centre in non-uniform circular motion. It has both radial and tangential components.

Angular kinematics (constant alpha): omega = $omega_0$ + alphat theta = $omega_0$t + $\frac{1}{2}$alpha$t^2$ $omega^2$ = $omega_0^2$ + 2alphatheta