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View Full Version : What is the speed of the minute hand on a clock?


Blayvis
03-11-2004, 03:46 AM
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:

dnooman
03-11-2004, 03:55 AM
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.

Richard Pearse
03-11-2004, 03:55 AM
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.

Mangetout
03-11-2004, 04:05 AM
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:
(2*pi*r)/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).

Mangetout
03-11-2004, 04:14 AM
Hmmm... I just plugged some real numbers into that calculation and the answer was clearly wrong.

Mangetout
03-11-2004, 04:15 AM
What a plank!

(2*pi*r)/3600 metres per second!

Mangetout
03-11-2004, 04:19 AM
So, for my wristwatch, which has an 11mm (0.011 m) minute hand, the speed of the tip is

(2*pi*0.011)/3600 = approximately 0.00002 metres per second or 0.02 (1/50th) millimetres per second.

Desmostylus
03-11-2004, 05:49 AM
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.

Mangetout
03-11-2004, 06:43 AM
It is probably a good thing, on the whole, that I don't work for NASA.

Mops
03-11-2004, 06:48 AM
Not to mention that with a lot of clocks it is exactly zero, most of the time.

tomndebb
03-11-2004, 06:49 AM
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.)

Mangetout
03-11-2004, 07:21 AM
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.

Desmostylus
03-11-2004, 07:24 AM
It is probably a good thing, on the whole, that I don't work for NASA.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.NASA's metric confusion caused Mars orbiter loss (http://cnn.com/TECH/space/9909/30/mars.metric/)

"The problem here was not the error, it was the failure of NASA's systems engineering, and the checks and balances in our processes to detect the error. That's why we lost the spacecraft."

aerodave
03-11-2004, 07:42 AM
it's 2*pi/hr

as in "2 pi radians per hour"

Noone Special
03-11-2004, 07:46 AM
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... :D

ducks and runs

Dani

dakravel
03-11-2004, 06:41 PM
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?

tomndebb
03-11-2004, 08:03 PM
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.

manson1972
03-11-2004, 08:13 PM
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?

Patty O'Furniture
03-11-2004, 08:14 PM
The next logical question is how fast does hair grow, in miles per hour?

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

Richard Pearse
03-11-2004, 08:24 PM
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?

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.

Mathochist
03-11-2004, 08:45 PM
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.

Actually, relativity comes in here and says that the force the atoms of the hand exert on the atoms farther out cannot propagate faster than a certain rate. This really long minute hand would bend as it tried to accelerate the tip. The hand in your wristwatch also bends, but imperceptably so.

On the other hand, if it were a laser rotating, the spot would move faster than the speed of light across a target placed farther than that distance away. This is because the image of the spot cannot carry any information from one side of the target to the other.

Jurph
03-12-2004, 12:28 PM
Hang on a second, Mathochist: the spot "moves", but from one second to the next, the spot is made up of different photons. Each photon in the laser's beam is moving at the speed of light in a purely radial direction; the rotation (at non-relativistic speeds) of the laser doesn't impart any circumferential momentum to them.

If you imagine a stationary laser firing a continuous stream of protons (imagine it as a PVC pipe with a long string of ping-pong balls, firing at a giant circular wall lined with bathroom scales, which will be our photon detectors). As you start rotating the dispenser, the ping-pong balls (photons!) that have already left the aperture are not going to rotate with it -- they're going to continue on in their path and hit the scale they were first aimed at. The beam will curve, and maybe even spiral (not sure on this!) so that your "spot" is not longer a spot. Eventually your ping-pong balls get so spread out that they will start "skipping" scales, or so that not enough of them hit each scale to make a detectable difference.

Mathochist
03-12-2004, 12:53 PM
If you imagine a stationary laser firing a continuous stream of protons (imagine it as a PVC pipe with a long string of ping-pong balls, firing at a giant circular wall lined with bathroom scales, which will be our photon detectors). As you start rotating the dispenser, the ping-pong balls (photons!) that have already left the aperture are not going to rotate with it -- they're going to continue on in their path and hit the scale they were first aimed at. The beam will curve, and maybe even spiral (not sure on this!) so that your "spot" is not longer a spot. Eventually your ping-pong balls get so spread out that they will start "skipping" scales, or so that not enough of them hit each scale to make a detectable difference.

It seems I didn't explain myself clearly. Yes, if you imagine a laser as a "photon gun" (which is really not quite the case, but close enough for hand waving), and imagine identifying "the" photons released from the laser as they travel outwards, that will trace a curve in space. What I was getting at is that there is no acceleration bending like there is in a solid minute-hand.

Imagine a hemispherical bowl one light-hour in radius (this is about three times as long as the critical distance mentioned before) centered on the laser's pivot. The laser will turn through the half-circle in 30 seconds. An hour after the experiment starts, the first photon "fired" by the laser will hit one edge of the bowl, followed by the others until 30 seconds later the last photon hits the opposite edge of the bowl. The spot has travelled pi light-hours in 30 seconds, but has not violated causality because there is no information the spot can move around. If one were to try this with a solid rod, the tip would never move faster than the speed of light.

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