Section 5

Circular motion

viz

\Delta\theta=\theta_f-\theta_i

The angular displacement is the difference between the final and initial angles.

viz

\omega_{\text{med}}=\frac{\Delta\theta}{\Delta t}

Ratio of the angular displacement to the elapsed time interval.

viz

\omega=\frac{d\theta}{dt}

Derivative of the angle with respect to time.

viz

v=\omega r

Linear speed in circular motion is the product of angular speed and radius.

viz

\omega=2\pi f=\frac{2\pi}{T}

Angular frequency is 2π times the frequency, or 2π divided by the period.

viz

a_c=\frac{v^2}{r}=\omega^2r

Also

a_c=\frac{4\pi^2r}{T^2}

Acceleration directed toward the center, of magnitude v²/r or ω²r.

viz

F_c=ma_c=\frac{mv^2}{r}=m\omega^2r

Net force toward the center equal to m v²/r, required for circular motion.

Note: it is not a new force; it represents the radial component of the net force.

viz

a_t=\alpha r

Tangential acceleration is the product of angular acceleration and radius.