# Clocks And Calendars Formulas

## Clocks

Minute SpacesThe face or dial of clock is a circle whose circumference is divided into 60 equal parts, named minute spaces.

Hour hand and minute hand: The smaller hand of a clock is called the hour hand or short hand and the larger one is called minute hand or long hand.

### Important Observations and Formulas of Clock :

• A clock is a complete circle having 360 degrees. It is divided into 12 equal parts i.e. each part is 360/12 = 300.
•  As the minute hand takes a complete round in one hour it covers 360 degrees in 60 min. Minute Hand covers 360/60 = 6 degree/ minute.
• Also, as the hour hand covers just one part out of the given 12 parts in one hour, this implies Hour Hand covers 300 in 60 min. i.e. 1/2 degree per minute.
• Therefore, the relative speed of the minute hand is 6 – (1/2) = 5(1/2)degrees.
• Every hour, both the hands coincide once. In 12 hours, they will coincide 11 times. It happens due to only one such incident between 12 and 1’o clock.
• The hands are in the same straight line when they are coincident or opposite to each other.
• When the two hands are at a right angle, they are 15-minute spaces apart.
• In one hour, they will form two right angles and in 12 hours there are only 22 right angles. It happens due to right angles formed by the minute and hour hand at 3’o clock and 9’o clock.
• When the hands are in opposite directions, they are 30-minute spaces apart.
• If a clock indicates 9.15, when the correct time is 9, it is said to be 15 minutes too fast. On the other hand, if it indicates 8.45, when the correct time is 9, it is said to be 15 minutes too slow.
• If both the hour hand and minute hand move at their normal speeds, then both the hands meet after 65(5/11) minutes.
• 22 times in a day, the hands of a clock will be in a straight line but opposite in direction.
• 44 times in a day, the hands of a clock will be straight.
• 44 times in a day, the hands of a clock are at right angles.
• 22 times in a day, the hands of a clock coincide. • When the minute hand is behind the hour hand, the angle between two hands at M minutes past H ‘o clock will be                                                                                         30(H-(M/5)) + (M/2)degree.
• When the minute hand is ahead the hour hand, the angle between two hands at M minutes past H ‘o clock will be                                                                                         30(H-(M/5)) – (M/2)degree

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