distinguish linear speed and velocity
Answers
There are similarities, but there is a fundamental difference: Linear velocity is relative. ... Whereas Angular Velocity, it's just how much rotations a body undergoes in a unit of time and since angular velocity is a vector quantity, it has a direction and magnitude.
Firstly, speed is a scalar quantity. This means it is something that simply has a magnitude. This means that for speed, we really don't care what direction we are going in, we only look at how fast we're going.
Velocity is a vector quantity. This means that both magnitude and direction is important. Hence, for velocity, we need to see how fast we are going and what direction we're going in (I.e. travelling forward and backwards is different)
Now that we've established that, let's assume you meant linear velocity and angular velocity. From the name itself, we can already see the difference - one being linear and one being angular. But what exactly do we mean by this?
Linear refers to motion in a straight line . For example, if you were to run from the first floor of a building to the top floor, we'd be moving linearly upwards.
Angular refers to a rotation . For example, it you were to take a ball on a string and swing it around in a circle, that would be referring to angular velocity.
It is useful to also look at the units of measurement. For linear velocity, it is meters per second while for angular velocity, it is radians per second (although radians is normally treated as unit less) hence we can see that the difference is that angular velocity is about changing angles while linear velocity is concerned with how far we're moving.
But these two concepts are connected as well. Lets assume we have a circle with radius rand there's a ball rotating along the circumference of the circle with angular velocity ω. Given that the ball travels one round around the circle, we can say that the angular distance travelled is 2π in radians and it's angular velocity is hence given by ω=2πt. Since it is moving in a circle, the distance that the ball travels after one round is 2πr and hence the linear velocity is given by v=2πrt.
Comparing these two formulae, we can now see that ω=vr. Hence, they are connected in some way by this formula. This formula also tells us that for a constant angular velocity (which makes sense for most cases because if we have a rigid object, all particles has to rotate at the same rate), the linear velocity increases as we go further away from the centre. Qualitatively, we can see that it travels a bigger circle when we are farther away while covering the same angle.