Watches

There is an old joke for those who still have analogue watches which consist of hands for second, minute and hour.

What did the second hand say to the hour hand as it went past? See you in a minute.

That begs a question. Precisely how long does it take the second hand to catch up with the hour hand?

The calculation is not as simple as it appears

Rpm is revolutions per minute

Note there are		1440	minutes in an hour
		60	seconds in a minute
	angular velocity
	Rpm
hour hand	0.000694444		= 1 / 1440	A
second hand	1			B
bring hour hand to halt by applying negative velocity,
means relative to hour hand                            angular velocity
	Rpm
hour hand	0			C	A - A
second hand	0.999305556			D	B - A
Thus time taken for hour hand and second hand to be aligned is
	1.0006949	minutes		=1/D
	60.041696	seconds

In other words see you in a minute is about right!