# Angular Velocity or Angular Speed?

1. Nov 14, 2011

### Sammy101

Hi,

We have been studying centripetal forces and accleration in my class, and my teacher has shown me how to derive centripetal acceleration as v^2/r using change in velocity over time. I recently got into angular velocity vs. linear velocity in my math class, and I know that angular velocity is the change in the central angle(in radians) over time. But is this not SPEED? Speed is distance traveled over time, which is like the change in the central angle. Velocity is change in displacement over time.

With this lack of clarity, I became confused with the formula for centripetal acceleration as change in velocity over time. The "velocities" we seemed to be using actually appear to me now as speeds.

So here are my two questions:
1) Should it be angular speed not velocity since it is really distance traveled around a circle over time and not displacement over time?
and
2) In the formula for centripetal acceleration, v^2/r, is the centripetal velocity suppossed to be termed centripetal speed since it is also the distance traveled around the circle over time? If not, then the displacement over time for an object traveling around a circle (velocity) is much less than the distance over time (speed), right?

2. Nov 14, 2011

### Sammy101

I think I had a slight enlightenment right when I posted this and I would like to clarify some things.
1) Angular velocity is the correct term because it is not the distance around the circle traveled over time (s/t) but rather the displacement over time which is not arc lenght over timer but theta over time. Right?
2)So in centripetal acceleration = v^2/r, they are using displacement over time for velocity right?, not arc lenght or "s" over time?
3)Is angular velocity the change in the central angle over time and angular speed the change in the arc lenght over time?

3. Nov 14, 2011

### khemist

What is the difference in velocity and speed? Well, the most obvious is the fact that speed is a scalar and velocity is a vector. In order to find the speed, we must take the square root of the sum of the squares of the components of the velocity (I think thats right). So angular velocity would be the speed at which an object is rotating, but it would have a direction, while the angular speed would simply be a number. Note that the speed is always positive, while velocity can be positive or negative depending on the coordinate axis.

In circular motion, there is certainly a displacement, but it is not simply dx. The displacement would actually be rdθ. It would not be m/s, but rather rad/s, or radians per second.

4. Nov 15, 2011

### sophiecentaur

The way an object moves on the end of a string will be due to the force which is 'towards' the centre of the string. This is in a particular direction i.e a vector quantity is involved so the rate of change of angle is also a vector quantity - a velocity.