Question

If you have $10.8$ meters per second, how do you convert that to radians per second?

Answer 1

Step-1: Formula used:

Angular velocity is given by

$\mathrm{\omega }=\frac{\mathrm{v}}{\mathrm{r}}$

where

$\mathrm{\omega }=$angular velocity

$\mathrm{v}=$ tangential speed

$\mathrm{r}=$radius

Step-2: Convert meter per second to radian per second

Given that,

$\mathrm{v}=10.8\mathrm{m}/\mathrm{s}$

It is known that,

$\mathrm{\omega }=\frac{\mathrm{v}}{\mathrm{r}}$ …(1)

Substitute $\mathrm{v}=10.8\mathrm{m}/\mathrm{s}$ and $\mathrm{r}=\mathrm{R}$ in equation(1).

$\mathrm{\omega }=\frac{10.8}{\mathrm{R}}\mathrm{rad}/\mathrm{s}$

Therefore, the value of meters per second is equal to $\frac{10.8}{\mathrm{R}}\mathrm{rad}/\mathrm{s}$.