The relation between linear speed v, angular speed `omega` and angular acceleration `alpha` in circular motion is

Explanation

Consider a particle performing circular motion in an anticlockwise sense, along a circle of radius r as shown in the figure. In a very small time interval `delta t`, the particle moves from point A to point B through a distance `deltas` and its angular position changes by `deltatheta`.
`therefore deltatheta=(arc AB)/(radius) = (deltaS)/(r) " "therefores= rdeltatheta`
THe linear speed v of the particle is the time rate at which the distance is covered by the particle. When `deltat to 0`, AB will be a straight line.
`v = (ds)/(dt)=lim_(deltat to0)(deltaS)/(deltat)=lim_(deltat to0)r(deltatheta)/(deltat)`
` =(lim_(deltat to0)(deltatheta)/(deltat))r`
`therefore v = (dtheta)/(dt)r" "...(1)`

The angular speed `omega` of the particle is the time rate at which the angle is swept out by the radius vector.
`therefore omega=(d theta)/(dt)" "...(2)`
From Eqs. (1) and (2), we get,
`v = omegar" "...(3)`
THus, linear speed = angular speed xx radius.