How long does it take for the clock to coincide with the minute hand, and when does the hour and min

Hello. According to the construction of the clock, we know that a circle is divided into 12 large grids, each of which represents 1 hour; At the same time, each cell is divided into 5 cells, that is, a circle is divided into 60 cells, and each cell represents 1 minute. In this way, it corresponds to the angle problem, that is, a large grid corresponds to 36 0° 12 = 30 °; A small cell corresponds to 360° 60 = 6°.

Now we take the direction of 12 o'clock as the beginning edge of the angle, and the direction of the hour hand of the two hands at a certain moment as the end edge of the angle, then the angle formed by the hour hand at the hour n minute is 30 (m+n 60) degrees, and the angle formed by the minute hand is 6n degrees, and the difference between these two angles is the angle between the two hands. If the degree of the two pointer clamps is denoted by , then =30(m+n 60)-6n. Considering that the relative positions of the two needles are front and back, in order to ensure that the angle sought is always positive and does not lose the solution, we give the following relation:

30（m+n/60）-6n|=|30m-11n/2|。

This is the formula for calculating the angle between two hands at a certain time, for example: find the angle between two hands at 5:40. Substituting m =5 and n =4 into the above equation gives =|150-220|= 70 (degrees).

This formula can also be used to calculate when the two pointers coincide and when the two pointers are at arbitrary angles. Because when the two hands coincide, the angle they are sandwiched is 0, that is, 0 in the formula, and then substituting the number of hours can find n. For example:

Find how many minutes the two hands coincide at 3 hours. Solution: Substituting =0, m=3 into the formula gets:

0=|30*3-11n/2|, the solution is n=180 11, that is, the two pointers coincide at 3:180 11. Another example: find 1 point and how many points are at right angles.

Solution: Substituting =90°, m=1 into the formula yields: 90=|30*1-11n/2|The solution is n=240 11.

The other solution is n=600 11).

The above formula can also be written as |30m+。Because the hour hand turns 30 degrees in one hour, it turns too much in one minute, and the minute hand turns 6 degrees in one minute.

The clock problem is the study of the relationship between the hour and minute hands on the clock face. The clock face is divided into 60 compartments. When the minute hand goes 60 squares, the hour hand goes exactly 5 squares, so the speed of the hour hand is 5 60 = 1 12 of the minute hand, and every 60 (1 5 60) = 65 + 5 11 (minutes) of the minute hand coincides once in the hour hand.

Here's a basic formula: the number of grids to catch up at the initial moment (1 1 12) = catch-up time (minutes), where 1 1 12 is the number of squares per minute that the minute hand travels more than the hour hand.

The hour and minute hands coincide at 12 o'clock or 24 o'clock。In 24 hours, the hour and minute hands coincide a total of 22 times, two of which coincide at the hour, that is, at 12 o'clock, and the remaining 20 times are not on the hour. The hour hand is the hand on the clock that indicates the hour, there are three hands on the clock, the longest is the second hand, the shortest is the hour hand, and the minute hand in the center of the length.

Hour hand summaryThe reason why the hour hand is clockwise.

The rotation is derived from its predecessor, the sundial.

The hour hand first appeared in the Northern Hemisphere.

It functions similarly to the shadow pointer cast on the ground by a sundial. The sun rises in the east and sets in the west, and the shadow it casts on the sundial moves in the opposite direction, from west to east, so the same is true of the arrangement of the numbers representing time on the sundial, which is the same arrangement of the numerals on the surface of modern clocks.

Whether an object rotates clockwise or counterclockwise depends on the angle of view. For example, the rotation of the Earth is counterclockwise from directly above the North Pole**, and clockwise from directly above the South Pole.

The minute and hour hands coincide at 12 o'clock or 24 o'clock. In 24 hours, the hour and minute hands coincide 22 times, two of which coincide on the hour, namely zero and 12 o'clock, and the remaining 20 times are not on the hour.

1 o'clock, 13:30 (another 5 11 minutes.)

2 o'clock, 2 p.m. 60 p.m. (10 11 p.m.)

3 o'clock, 15:90 (4 11 minutes.)

4 o'clock, 16 o'clock 120 (again 9 11 minutes.)

5 o'clock, 17 o'clock 150 (again 3 11 minutes.)

6 o'clock, 18 o'clock 180 (again 8 11 minutes.)

7 o'clock, 7 p.m. 210 (again 2 11 minutes.)

8 o'clock, 20 o'clock 240 (again 7 11 minutes.)

9 o'clock, 21 o'clock 270 (again 1 11 minutes.

10 o'clock, 22 o'clock 300 (again 6 11 minutes.)

12 o'clock and 24 o'clock.

The difference between the minute hand and the hour hand1. The length is different. The minute hand is longer than the hour hand.

2. Different thicknesses. Generally, the thicker is the hour hand, and the thinner is the minute hand.

3. The rotation rate is different. It takes 12 hours for the hour hand to make one revolution, and one hour for the minute hand to make one revolution. The hour hand moves in hours, the minute hand moves in minutes, and the minute hand moves for one minute for every small block on the clock.

4. The meaning of the representation is different. The hour hand represents the number of points and hours of time, and the minute hand represents the number of minutes.

Every time the clock reaches 0:00 or 12:00, the minute hand and the hour hand coincide.

1. At 0 o'clock and 12 o'clock, the minute hand and the hour hand coincide, as shown in the following figure

2. At 6 o'clock and 18 o'clock, the hour hand and the minute hand form a straight line, as shown in the following figure

Expansion of information training punching:1. Characteristics of the hands on the clock face:

1. Length: The second hand is the longest, the hour hand is the shortest, and the minute hand length is between the two.

2. Running speed: the second hand is the fastest, the hour hand is the slowest, and the minute hand is in between.

3. The width of the yard in the hole: Generally speaking, the second hand is the thinnest, the hour hand is the thickest, and the minute hand is in between.

2. Conversion relationship of time units:

1. One day = 1440 minutes, 1 hour = 60 minutes, 1 minute = 60 seconds.

2. One moment = 15 minutes, one word = 5 minutes (southern Fujian.

Guangdong regional usage).

To calculate the hour, the hour and minute hands coincide at 12 o'clock; At 6 o'clock, the minute hand and the hour hand form a straight line; At 3 o'clock or 9 o'clock, the minute hand and the hour hand form a right angle.

The hour and minute hands overlap 22 times a day, and if the time of the hour and minute hands of a clock coincides at 12 o'clock, it coincides again every 360 (and 5 11 (minutes). Number of overlaps in a day: 24 * 60 (65 and 5 11) = 1440 * 11 720 = 22 times.

22 analyses coincided in one day.

Because the angle of the center of the circle rotated by the hour hand for 1 minute is degrees, and the angle of the center of the circle rotated by the minute hand for 1 minute is 6 degrees, when the two needles coincide for the first time and then coincide for the second time, the number of angles of the center of the circle rotated by the minute hand is 360 degrees more than that of the socks and the hour hand, so the time required for the two needles to coincide again is: t = 65 + 5 11 minutes.

This kind of problem is actually the pursuit problem of the minute hand chasing the hour hand, and its formula is: t=s (v1-v2), s=60 (d), minute hand speed: v1=1 dg minute, hour hand speed:

v2 = 1 12 square minutes, therefore, the calculation obtains t t = 65 + 5 11 minutes, according to the above calculation, every 65 + 5 11 minutes the hour hand and the minute hand coincide. That is, from 12 o'clock, every 65 + 5 11 minutes, the hour hand and the minute hand coincide once, and the whole day coincides a total of 22 times.

Every time the clock reaches 0:00 or 12 o'clock, the minute and hour hands coincide.

1. At 0 o'clock and 12 o'clock, the minute hand and the hour hand coincide, as shown in the following figure

Second, at 6 o'clock and 18 o'clock, the hour hand and the minute hand form a straight line, as shown in the following figure:

Based on strict time calculation (i.e., 00:00-23:59 every day), the hour hand turns 2 times a day, the minute hand turns 24 times a day, and the instant hand coincides with the minute hand 22 times every 24 hours, that is, the minute hand and the hour hand 12 11 hours overlap into one banquet, which is about equal to 1 hour, 5 minutes and 5 seconds.

Let the minute hand coincide with the hour hand after t minutes, then the radian of the minute hand is t 60*2, and then the number of coincidences is n, then the noisy arc of the hour hand is t 60*1 12*2 + (n-1)*2, so there is t 60*2 = t 60*1 12*2 +n*2 that is, n=t*11 720+1,n n. After finding the analytic formula of the function, you can easily answer the question, such as when t=300 (five hours), n=5 is calculated from the first coincidence of the opening at 0 o'clock, and the hour and minute hands coincide 5 times after five hours; When t=1440 (a whole day), n=23 means that the hour and minute hands coincide 23 times in a day; When n=9, t=, i.e., the ninth coincidence time is about 8:44.