Question

What is the angular velocity of an object traveling in a circle of radius 0.75 with a linear speed of 3.5m/s?

Answer 1

The angular velocity $\omega$ is $\omega = \dfrac{V}{R} = \dfrac{3.5\,\mathrm{m/s}}{0.75\,\mathrm{m}} \approx 4.67\,\mathrm{rad/s}.$

Why is this formula correct? The angular velocity $\omega$ is $\omega = \dfrac{2\pi}{T} = \dfrac{2\pi}{2\pi R/V} = \dfrac{V}{R}.$