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!
