At What Time Do Hour and Minute Needles Coincide After 12'O Clock?

  • Thread starter sheperd
  • Start date
In summary, the conversation discusses the coincidence of the hour and minute hands on a clock and the formula for calculating the angle of each hand. The first coincidence occurs at 1:05:27.2727, but the question remains if the second hand can also coincide with them at the same time.
  • #1
sheperd
4
0
Hi

I just want to know in a clock, 12’O clock both needles (hour and minute) will coincide (one over the other)
My question is exactly at what time both needles will coincide again after 12’o clock

Good luck.
 
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  • #2
13.05 :shy: ?
 
  • #3
movement of hourhand:
hour hand moves 360 degree in 12 hours.
one hour is 30 degree. or 60 minutes =30 degree movement
6 minutes = 3 degrees
one minute= .5 degrees.
5 minutes =2.5 degrees

minute hand moves 360 degrees in 60 minutes
5 minutes = 30 degrees
one minute =6 degrees
at 1:05 the hour hand is at 32.5 degrees . minute hand is at 30 degrees
 
  • #4
Let [itex]\theta_h[/itex] be the angle of the hour hand away from the 12, and [itex]\theta_m[/itex] be the angle of the minute hand away from the 12. Then I think you can see that
[tex]12\,\theta_h=\theta_m+360^\circ n[/tex]
where n is an integer. Now set [itex]\theta_m=\theta_h[/itex] and solve for each n. For example, the first coincidence is at [itex]\theta_{h,m}=360^\circ/11[/itex], or 1:05:27.2727...
 
  • #5
Yes, but can you do it with hour, minute and second hands all coinciding? :-)
 
  • #6
12:00
this is the only answer...
 
  • #7
Can you prove it? :-)
 

1. How does the time of the hour and minute needles coinciding change throughout the day?

The time of the hour and minute needles coinciding changes throughout the day because the minute hand moves continuously while the hour hand moves in increments. This means that the time they coincide will vary depending on the hour hand's position.

2. Is there a specific pattern or formula to determine when the hour and minute needles will coincide?

Yes, there is a specific pattern to determine when the hour and minute needles will coincide. The formula is: (11 * minutes) / 2 = hours. This means that for every 60 minutes, the hour hand moves 30 degrees while the minute hand moves 360 degrees, resulting in a difference of 330 degrees. This difference is divided by 2, resulting in the number of hours the hour hand needs to move to coincide with the minute hand.

3. Can the hour and minute needles coincide more than once in a day?

Yes, the hour and minute needles can coincide more than once in a day. This will happen when the hour hand makes a full rotation while the minute hand is moving, resulting in multiple coinciding times.

4. What is the significance of the hour and minute needles coinciding?

The hour and minute needles coinciding has no significant meaning in terms of timekeeping. It is simply a mathematical occurrence based on the movements of the clock hands.

5. How can I calculate the time when the hour and minute needles will coincide?

To calculate the time when the hour and minute needles will coincide, you can use the formula mentioned in question 2. You can also use a clock or watch with hour and minute hands to visually determine the coinciding time.

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