: What is angular velocity?
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*tl;dr: Angular velocity is the vector form of the rate of change of something’s angle. You measure the angle something is at, you work out how that angle is changing over time, and then you include the direction it is changing in.*
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If we have something that is repeating in a pattern it can be useful to describe where it is at the moment in the pattern (rather than where it is absolutely).
For example, time comes in a whole bunch of repeating patterns (seconds in a minute, minutes in an hour, hours in a day, days in a week, days in a year, months in a year and so on). Rather than counting time as an absolute number (like UNIX time – the number of seconds since 1 January 1970) we care about where we are in a particular cycle – how many minutes past the hour, how many hours into a day and so on. And with any of these we can measure where we are in a cycle in terms of the “angle” it would make if our cycle was a circle, so where 0° would be the start, 90° a quarter of the way through, 180° halfway through and 360° back to the start again (although in maths, physics and engineering we’d usually use radians rather than degrees). This is how analogue clocks work. Each hand is representing how far through the minute, hour or half-day we are as an angle.
Normal speed tells us how a distance changes over time. *Angular* speed then tells us how quickly our angle is changing – for example how many degrees per second. The second hand on a clock moves at an angular speed of 360° per minute, or 6° per second (each second “tick” is 6° from the previous one). We could also measure it in terms of the frequency; how many complete cycles we get through in a time period. A second hand moves at 1 RPM (one complete rotation per minute), or 1/60 Hz (rotating 1/60th of a circle per second).
Angular *velocity* takes this a step further, by turning quantity into a vector, not just a number. Angular velocity would be the same as the angular speed, but would also tell us which way around our thing is cycling (so on a clock, the second hand moves with an angular speed 6° per second, but an angular velocity of 6° per second *clockwise*). Mathematically encoding this information in the term – rather than having to mention it separately – makes calculations a lot easier, and lets us do all sorts of sneaky things.
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One common uses of angular velocity is when things are moving, and we care about how they are moving around a point, rather than in a particular direction. Often because the thing is moving in a circle, but sometimes just because we care about that fixed point. In that case, angular velocity directly links to the normal “linear” velocity (i.e. movement through space), but is telling us the same thing as above; how is the angle the object is at changing over time, and in which direction.
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