Question

Define angular velocity and angular acceleration. Obtain relation between linear velocity and angular velocity.

Answer 1

Angular velocity is the rate of velocity at which an object or a particle is rotating around a center or a specific point in a given time period. It is also known as rotational velocity. Angular velocity is measured in angle per unit time or radians per second $\frac{rad}{s}$. The rate of change of angular velocity is angular acceleration

ds=vdt

$\frac{d\theta }{dt}$=$\frac{v}{r}$

angular velocity $\omega$ =$\frac{v}{r}$

in vector notation,$\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$