derive the relation between linear and angular velocity .I will mark as brainlist
Answers
Linear velocity is simply how fast, and in what direction an object is moving (in SI units this is expressed in metres per second) relative to some frame of reference. Something which is moving in a straight line at constant speed is said to be in an inertial frame of reference (that is there is no acceleration).
In contrast, angular velocity is the rate at which an object is rotating around an axis (angular displacement over time). It is often expressed in radians per second although it could equally be expressed in degrees or total revolutions in a time period. Indeed the units can be reversed - we might say that the Earth orbit the Sun once every three hundred and sixty-five and a quarter days. (nb. a pedant will point out that the Sun and Earth actually rotate around a common point, but as that common point is well within the bounds of the Sun, it is usual to describe the Earth as orbiting, or going around the Sun).
What is also inherent in any object rotating around an axis is that it is undergoing a continual acceleration towards that axis. If (like the moon) that acceleration towards the centre is such that (over time) it will maintain much the same distance from the point it it rotating around, it can be said to be in orbit. If the acceleration is insufficient it will fly off in some other direction. Something which has angular momentum is inherently in a non-inertial frame of reference (but see later).