What is the speed of the minute hand on a clock?

You can never seem to see the minute hand move. I was looking at my clock the other day and figured i’d ask the Straight Dope board about the speed of the minute hand… So, get to it. :cool:

Is it .016666… rpm? Maybe I did the math wrong. One sixtieth of an RPM, sixty times slower than the 1 RPM of the second hand.

One revolution per hour.

Seriously, that is the only meaningful way you can assign a speed to a generic minute hand. The linear speed of the minute hand is different depending on where along it’s length you’d like to measure, and how long it is. A long minute hand on a big clock will have a much higher speed than a small minute hand on a watch.

If you really want the speed of the minute hand of specific time piece then work out the circumferance of the clock face. The speed is that distance per hour.

Find a clock with a really large face (i.e. one that has really long hands) and you’ll be able to see the tip of the minute hand moving quite easily.

The speed of the tip of the minute hand is:
(2pir)/360 metres per second, where r is the distance in metres from the tip of the minute hand to the centre of the hub (I was going to just say the ‘length’ of the minute hand, but sometimes it extends on both sides of the hub for balance).

Hmmm… I just plugged some real numbers into that calculation and the answer was clearly wrong.

What a plank!

(2pir)/3600 metres per second!

So, for my wristwatch, which has an 11mm (0.011 m) minute hand, the speed of the tip is

(2pi0.011)/3600 = approximately 0.00002 metres per second or 0.02 (1/50th) millimetres per second.

The minute hand on the Big Ben clock is about 4 m long. Plugging that number into Mangetout’s formula gives a tip speed of about 0.007 m/s, or 7 mm/s, or 0.025 km/h.

It is probably a good thing, on the whole, that I don’t work for NASA.

Not to mention that with a lot of clocks it is exactly zero, most of the time.

Of course, tthen you get the clock makers who do not simply let the minute hand move continuously, letting it sit still, then jerking forward once each minute. Which speed do you measure there? (I’d go for 1 rph.)

Even on watches where the minute hand ‘ticks’, the average speed over the whole hour is going to be the same formula - it has to be.

Why? It took you about 10 minutes to test the formula and correct it. It’s not like you caused a space probe to crash into Mars, or anything.

it’s 2*pi/hr

as in “2 pi radians per hour”

OK, now that the question is answered, let’s have some fun…

How fast does the minute indicator on my watch move?

Datum: I have a digital watch… :smiley:

ducks and runs

Dani

Or how about, how long would the minute hand have to be such that the very tip of the minute hand was moving at the speed of light?

At 669,600,000 miles per hour, using 3.14159265 as pi, it would need to be 213,140,300.032+ miles long. Of course, since the tip would be moving at the speed of light while the axis was stationary, we would run into a bit of a problem in which the tip and axis had not experienced the same hour.

Hello all.
The above made me think of a question I’ve had for a long while. If you shrunk yourself down so much in scale that the minute hand just looked to you like it was that long (213,140,300.032+ miles) would you measure the speed as the speed of light? Or does relativity jump in?

The next logical question is how fast does hair grow, in miles per hour?

(Answers in KPH are acceptable if you are Mangetout.)

Relativity doesn’t work that way. If you made yourself smaller then your watch hand may appear to be huge, but it would still just be a cm long or so.

You could redefine distance to stay relative to you and then you could say that the watch hand was 213,140,300.032 miles long. But then you’d have to redefine the speed of light to compensate.

The speed of light is not slower for small things.