Answer to Puzzle # When the Hands of a Clock First Overlap
How many times a day do the Hour, Minute, and Seconds hands of an in an hour whilst the hour hand moves one hour, which is 1/12th of the clock face). A regular clock has an hour and minute hand. At 12 midnight the hands are exactly aligned. When is the next time they will exactly align or overlap? How many. You can figure out that this corresponds 5 minutes, 27 and 3/11 seconds If it is 1 o clock, the hour arm is 30 degrees ahead of the minute arm.
Save A wall clock showing the time at In its most basic form, recognized throughout the world, the periphery of the dial is numbered 1 through 12 indicating the hours in a hour cycle, and a short hour hand makes two revolutions in a day. A long minute hand makes one revolution every hour.
The face may also include a second hand, which makes one revolution per minute. The term is less commonly used for the time display on digital clocks and watches. A second type of clock face is the hour analog dialwidely used in military and other organizations that use hour time.
This is similar to the hour dial above, except it has hours numbered 1—24 around the outside, and the hour hand makes only one revolution per day. Some special-purpose clockssuch as timers and sporting event clocks, are designed for measuring periods less than one hour. Clocks can indicate the hour with Roman numerals or Hindu—Arabic numeralsor with non-numeric indicator marks.
- Two Clocks
- Answer to Puzzle #35: When the Hands of a Clock First Overlap
- The Hands of Time The long hand is the minute hand.
The two numbering systems have also been used in combination, with the prior indicating the hour and the latter the minute. Longcase clocks grandfather clocks typically use Roman numerals for the hours. Clocks using only Arabic numerals first began to appear in the midth century. The clock face is so familiar that the numbers are often omitted and replaced with applied indices undifferentiated hour marksparticularly in the case of watches. Occasionally, markings of any sort are dispensed with, and the time is read by the angles of the hands.
Reading a modern clock face ' In the analog clock, the minute hand is on "14" minutes, and the hour hand is moving from "12" to "1" - this indicates a time of A ship's radio room wall clock during the age of wireless telegraphy showing ' The time is read by observing the placement of several "hands", which emanate from the centre of the dial: A short, thick "hour" hand; A long, thinner "minute" hand; On some models, a very thin "second" or "sweep" hand All the hands continuously rotate around the dial in a clockwise direction — in the direction of increasing numbers.
The second, or sweep, hand moves relatively quickly, taking a full minute sixty seconds to make a complete rotation from 12 to For every rotation of the second hand, the minute hand will move from one minute mark to the next. The minute hand rotates more slowly around the dial. It takes one hour sixty minutes to make a complete rotation from 12 to For every rotation of the minute hand, the hour hand will move from one hour mark to the next.
The hour hand moves slowest of all, taking twelve hours half a day to make a complete rotation.
And not necessary to solve the problem. The first line of our equation then becomes: It's difficult to divine this. But it makes sense. Just as we reasoned our first overlap will be at just after 1: Our overlaps will be at just after 1: A Very Scientific Approach below also gives us a way to realise this. I found the whole problem a lot easier to visualise by playing with the flash based clock below.
You can drag the hands with your mouse.
Aligned Clock Hands
Click here to view flash content I want to look at the concept of reference frames, the idea has many applications in physics, it's essential for example in general relativity or when we consider something like how fast is the light traveling away from the head lights of a fast moving car.
But it also has some much more mundane applications. Simply we redefine our co-ordinate system so that it's stationary with respect to one of our bodies. An example of this would be if we have two cars moving at different speeds, lets say 30 and 35mph.Learn How to Tell Time on a Clock
The faster car is a mile behind, when will it overtake? In this reference frame the lead car is stationary and the car behind is a mile away approaching at 5mph. That's essentially a one dimensional problem and a bit too easy to solve.
Two Clocks : jingle-bells.info
But if you are considering say the intercept courses of ships in two dimensions it becomes more useful. We will make our reference frame that of the Hour Hand. The problem will exist from the perspective of someone stood on the Hour Hand with no other visual cues; all he can see is the minute hand.
To move into the frame of reference of the Hour Hand we subtract it's speed from that of the Minute Hand to give the Minute Hand's speed in the Hour Hand's reference frame. Coincidence or overlap occurs every time the Minute Hand makes a complete revolution.