What are the similarities and differences between the hour and minute hands on the clock face?

Similarities between the hour hand and the minute hand:

1) The clock and minute hand are an important part of clockwise rotation;

2) The angular velocity (period) of rotation is fixed, and the center of rotation coincides.

Difference Between Hour and Minute Hands:

1) Different lengths and thicknesses.

To make it easier to identify the time, the length of the hour hand is usually shorter, and the length of the thin hand is also longer. The hour hand is thick, and the minute hand is thin.

2) Different speeds.

Minute hand speed: 1 block per minute, 6 degrees per minute; Minute hand speed: 1 12 divisions per minute, degrees per minute.

The hour hand rotates one scale per hour, i.e. 15 degrees, and the minute hand rotates 12 scales per hour, i.e. 360 degrees. In a day, the number of revolutions of the hour hand is greater than the number of revolutions of the minute hand.

3) Different representational meanings.

The hour hand indicates the number of points in time, that is, 2 o'clock, 3 o'clock; The minute hand points to the scale that indicates the number of minutes in the hour, i.e. 2:20. 2:30 a.m. and so on.

1. The similarities between the hour hand and the minute hand.

Both the hour and minute hands are important parts of a clock; All rotate clockwise; The scales from 1 to 12 on clocks have their own meanings; The angular velocity of rotation (period) is fixed; The center of the rotation coincides.

2. The difference between the hour hand and the minute hand.

1. The shape is different.

In order to make it easier to identify the time, the length of the hour hand is generally shorter and the length of the minute hand is longer. The hour hand is thicker and the minute hand is thinner.

2. The speed is different.

Minute hand speed: 1 small block per minute, 6 degrees per minute; Hour hand speed: 1/12th of a square per minute, 1/20 per minute.

The hour hand rotates one scale per hour, i.e. an angle of 15 degrees, and the minute hand turns 12 scales per hour, i.e. an angle of 360 degrees. In a single day, the number of revolutions of the hour hand is greater than the number of revolutions of the minute hand, which can be made twice and the minute hand 24 times.

3. The meaning of the representation is different.

The hour hand represents the number of points in time, that is, 2 o'clock, 3 o'clock; The scale pointing to the minute hand represents the number of minutes in the hour, i.e. 2:20. 2:30 a.m. and so on.

Same: Lap timing.

Difference: one rotation of the hour hand is 12 hours, and one hour of one rotation of the minute hand. It took 12 turns of the minute hand to make one turn.

Similarities: Walking around is 360°, which is a unit of quantity.

The difference: the hour hand goes around for an hour, and the minute hand goes around for a minute. The length is also different, making it easy to distinguish.

The minute hand is a little longer than the hour hand.

When the hour and minute hands coincide on the clock face, the time indicated may be 12 o'clock.

Several key angles on the dial of the clock:

1) 9 o'clock in the morning: the hour and minute hands are at an angle of 90 degrees.

2) 12 noon sharp: the hour and minute hands are at an angle of 0 degrees.

3) At 3 p.m., the hour and minute hands are at an angle of 90 degrees.

4) 6 p.m. sharp: The hour and minute hands are angled at 180 degrees.

Conversion relationship for time units:1) One day = 1440 minutes, 1 hour = 60 minutes, 1 minute = 60 seconds.

2) One moment = 15 minutes, one word = 5 minutes (usage in southern Fujian and Guangdong).

Relationship between the angles of each hand of the clock:

1) An ordinary clock is equivalent to a circle, and its hour or minute hand is equivalent to walking at a 360° angle.

2) The angle of each large cell on the clock is: 30°.

3) The angle corresponding to each 1 minute of the hour hand should be:

4) The angle of the minute hand should be 6° for every 1 minute.

When the hour and minute hands coincide on the clock face, the time is 12 o'clock.

The hour and minute hands on the clock face coincide exactly 11 times. The timing of each overlap is different, and the minute hand speed is "1", and the hour hand speed is 1 12 of the minute hand speed, and the minute hand is 11 12 of the minute hand faster than the hour hand.

Between x o'clock and (x+1) o'clock, the hour and minute hands on the clock face coincide exactly: 5x (11 12) = (60x) 11 (minutes), x takes ....11。

Between 1 o'clock and 2 o'clock, the hour and minute hands on the clock face coincide exactly: 5*1 (11 12) = 60 11 (minutes); Between 2 o'clock and 3 o'clock, the hour and minute hands on the clock face coincide exactly: 5*2 (11 12) = 120 11 (minutes).

Between 3 o'clock and 4 o'clock, the hour and minute hands on the clock face coincide exactly: 5*3 (11 12) = 180 11 (minutes); Between 11 o'clock and 12 o'clock, the hour and minute hands on the clock face coincide exactly: 5*11 (11 12) = 60 (minutes), that is, exactly at 12 o'clock.

On the clock face are the hours of three and nine, and the minute and hour hands are at right angles.

1) At 10 o'clock in the morning, the hour hand on the clock face is pointing to 10, the minute hand is pointing to 12, and the middle is 2 large grids, so at 10 o'clock in the morning, the angle between the hour hand and the minute hand is 30 ° 2 = 60 °, which is an acute angle;

2) At 4 o'clock in the afternoon, the hour hand on the clock face is pointing to 4, the minute hand is pointing to 12, the middle is 4 large squares, and the angle formed by the hour hand and the minute hand is 30 4 = 120 °, which is an obtuse angle;

3) The angle formed by the hour hand and the minute hand is a right angle, only the hour hand points to 12, and the minute hand points to 3 or 9 o'clock, and the angle formed by the hour hand and the minute hand is a right angle, so at 3 o'clock or 9 o'clock, the angle formed by the hour hand and the minute hand is a right angle.

On the clock face are the hours of three and nine, and the minute and hour hands are at right angles.

On the clock face are three and nine o'clock, and the minute hand and ten are at right angles!

12 o'clock to 3 o'clock, 3 o'clock to 6 o'clock, 6 o'clock to 9 o'clock, 9 o'clock to 12 o'clock.

The hour and minute hands coincide at (12) o'clock. When the hour and minute hands form a line, it is (6) o'clock.

There are 12 large squares, 60 small squares, and 1 large square with 5 small squares. The hour hand travels 1 block for 1 hour, the minute hand moves 1 block for 1 minute, and the minute hand moves 1 block for 5 minutes.

Several key angles on the dial of the clock:

9 o'clock in the morning: the hour and minute hands form an angle of 5261 degrees at 90 degrees. 12 o'clock sharp:

The hour and minute hands are angled at 0 degrees. 3 p.m. sharp: The hour and minute hands are angled at 90 degrees.

6 p.m. sharp: The hour and minute hands are angled at 180 degrees.

Since 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 more than the hour hand is 360 degrees, so the time required for the two needles to coincide again is:

t=65+5 11 minutes, this kind of problem is actually a chasing problem of the minute hand chasing the hour hand, and its formula is:

t= s (v1-v2), s=60 (d), minute speed: v1=1 d/min, hour hand speed: v2= 1 12 d/min, so, t=65+5 11 minutes, according to the above calculation, the hour hand and minute hand coincide every 65+5 11 minutes.

That is, from 12 o'clock, every 65+5 11 minutes, the hour hand coincides with the minute hand once, and the whole day coincides 22 times. There are 24 60 = 1,440 (minutes) in one day and night, so two needles coincide 22 times in one day and night.

The number of coincidences = 1440 (65 + 5 11) = 22 times, respectively: 1 hour, 13 hours 30 (again 5 11 points.

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

3 o'clock, 15 o'clock 90 ) and 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.

1) An ordinary clock is equivalent to a circle, and its hour or minute hand is equivalent to walking at a 360° angle.

2) The angle of each block on the clock (one hour of the hour hand or five minutes of the minute hand) is: <>

3) The angle corresponding to every 1 minute of the hour hand should be: <>4) The corresponding angle of the minute hand for every 1 minute should be: <>When the time is m point n minutes, the degree of the angle between the hour hand and the minute hand is:

1) The minute hand is in front of the hour hand:

(2) The minute hand is behind the hour hand:

The time point m=1,2,..12. Substitute the above two formulas respectively to find n.

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 o'clock 90 ) and 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.