How often is the speed of rotary motion measured in terms of linear distance traversed rather than angle swept? I can’t think of any, but perhaps you have some example in mind that compels you to not want to use angular speed.
If anyone want to defend their answer of 24, they’re welcome too. The 24-hour clocks around here simply double-mark each hour tick with two numbers (0-12, 1-13, 2-14, etc.). I’ve never seen in real life a clock with 24 hour ticks.
We have them at work showing the time in our offices around the world. More decorative than functional, I find them incredibly annoying because I have to look at the numbers to figure out what time they show.
That is an interesting question, but harder than the simple on I asked. I don’t expect most people to get it correct–I was suggesting a real-life math question everyone should get right.
I failed. 
22. The minute hand passes the hour 11 times per half day, when the hour hand is exactly at 12, then between 1 and 2, then between 2 and 3, then between 3 and 4, … and finally between 10 and 11.
Wouldn’t it be 23? Midnight counts as 1, not 0
Damn, I really am having a bad day
Yeah, I fell into the trap, too. Good one!
It’s the dope; pointless nitpicking is part of the fun. I was tempted to ask about the relative lengths of the hands too, until I saw Gorsnak had gotten there first.
In any case, the response to your request for an example is your car, where the speed of rotary motion of your wheels is measured to produce a linear measure of distance of travelled for the sake of your speedometer.
Here’s another way of thinking of it:
During a full day, the hour hand does two complete “laps”, while the minute hand does 24. Thus the minute hand must meet or pass the hour hand 22 times within the day.
I hate the poll answers. My answer is
the minute hand moves 12 times as fast as the hour hand. I hope that expressions of the form “X times more than Y” never pop up in technical publications.
I stand proudly when I say I got it 100% wrong.
I hate math, I’m terrible at math, and there are precisely zero real-world applications for this question, so I threw out the answer I figured it would be and was (unsurprisingly) wrong.
If the health and well being of my entire family came down to me getting a math problem right then I would wonder just how long it would take for me to get a new family
Well, if you start and finish at midnight, and count both of them, it’s 23. But I think really you should only count one of them.
If you start and finish at five past midnight, then the hands will cross 22 times, unambiguously.
If you start at midnight, and run for 1000 days, the hands will cross 22001 times if you count both the start and the end. That’s virtually equal to 22 times per day, as near as makes no difference.
So I’d say 22 times is the correct answer.
Why do you refuse to accept it? Angular velocity is a well defined and heavily used concept. Sure, there are multiple ways of measuring speed, but refusing to accept angular velocity puts you in Time Cube guy and Terence Howard 1x1=2 territory.
How many of you already know, without stopping to do any math or logical consideration (in other words you’ve relied on this knowledge) the time it takes for the hour hand to move from one of the little “minute” tickmarks to the next?
Am I the only person who looked at it like “The second hand covers 360 degrees in the time that it takes the hour hand to cover 30 degrees. 30/360 = 1/12, or 12 times faster”?
And Gorsnak, you’re wrong- if you look at it from the perspective I did, how the hands are delineated doesn’t matter; it’s still a situation where the shorter hand covers a 30 degree sweep in the same amount of time that the longer hand covers a full 360 degree rotation, or 12 times faster.
When starting at midnight I think 23 or 24 could be considered the correct answer, depending on how one defines “pass”. On a 24 hour clock, if we start at 00:00 both of the hands are aligned, pointing straight up. At 00:01 the minute hand has moved beyond the hour hand. Is that a “pass”? In my mind it is, just as a quick runner could be said to have passed their opponent right out of the gate. The minute hand then passes the hour hand 23 additional times - 1:01 through 23:01, inclusive. The time period expires at 24:00, when the hands are once more aligned. Starting with the hands aligned and calling the first movement a “pass” means 24 passes per day. If pass is strictly defined as “moving from behind to ahead” it would be 23.
That start time (or any where the hands do not start in alignment) would result in 23 passes. Starting the 24 hours at 00:05 means that the minute hand will not pass the hour hand the first time until 01:06. Twenty-two additional passes will occur - 02: 06 through 23:06, inclusive.
My first instinct was “60 times” but knowing how awful at math I am, I knew it was wrong. I don’t understand *why *it’s wrong, I just knew it was to obvious to be the correct answer.
It’s wrong because the minute hand and hour hand use different scales on the circle. The minute hand passes 60 increments in a single revolution. The hour hand passes only 12 increments in a single revolution. If the hour hand used the same scale, it would indeed be a 60x difference, but it would take 2 and a half days for the hour hand to make a full revolution.
I knew it takes one hour for the hour hand to move between the numbers which covers 5 minutes for the big hand, so it must by 60/5, but I’m bad at math so I worked it out a little more before answering.
I stand proudly when I say I got it 100% wrong.
However, I love math, am good at math, and use math on a daily basis.
I’m just an idiot… who answers before she thinks sometimes.
It’s a great question, though.
Nope. either 22 or 23, but certainly not 24.
No, 22.
The hands will cross at approximately the following times, give or take a minute
1.05, 2.11, 3.16, 4.22, 5.27, 6.32, 7.38, 8.43, 9.48, 10.54, 12.00
That’s 11 times every 12 hours, or 22 per day.
Try it for yourself if you don’t believe me. Get an old watch, wind the hands forward 24 hours, and count how many times the hands cross.