Clock Concepts - SEAAP005 - Shoolini U

Clock Concepts

1. Introduction to Clocks

A clock is a circular structure divided into 12 equal parts, representing hours, with 360° around the face. Time and angles between clock hands are calculated using geometric principles.

2. Key Concepts

3. Formula to Calculate Angle Between Hands

The angle between the hour and minute hands can be calculated as:

$$\theta = |(30H - 5.5M)|$$

Explanation:

The absolute value ensures the angle is always positive.

4. Types of Angles in Clock Problems

Example: If the angle between hands is \(120°\), the larger angle is \(360° - 120° = 240°\).

5. Example: Finding Angle Between Hands

Problem: Calculate the angle at 3:15.

Solution:

6. Finding Time From a Given Angle

To find the time when a specific angle is given:

Example: Find the time when the angle between hands is \(90°\) at 3:00.

Solution:

7. Coincidence of Hands

Hands coincide (overlap) when their angle is \(0°\).

Formula:

$$M = \frac{60H}{11}$$

8. Hands Perpendicular to Each Other

The hands are perpendicular when the angle is \(90°\).

9. Example: Hands Coincide Between 2 and 3

Problem: Find when the hands overlap between 2 and 3.

10. Summary of Key Formulas