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Change in Speed:
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- Acceleration is usually associated with a change in the speed of an object.
- However, it’s crucial to understand that a change in the direction of an object’s motion, even if its speed remains constant, also constitutes acceleration.
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Simplifying Circular Motion :
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- A runner sprinting around a track. On a rectangular track, if the athlete maintains a constant speed on each straight section (AB, BC, CD, DA), the only time his velocity changes is when he rounds a corner.
- Here, he alters his direction four times during a single lap.
- Modifying Track: Now, let’s modify the track’s shape. Suppose it’s hexagonal. On such a track, the runner adjusts his direction six times in a complete loop.
- If we shift to an octagonal track, the turns become more frequent — the athlete changes his direction eight times in one loop.
- Increasing Numbers: The intriguing part comes when we keep increasing the number of sides on our track.
- As the number of sides approaches infinity, each side becomes infinitesimally small, and our shape morphs into a circle.
- Example: For an athlete maintaining constant speed on a circular track, the only fluctuation in his velocity stems from the continuous shifts in direction.
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Accelerated Motion
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- This movement, despite the speed being unaltered, is termed as accelerated motion due to the constant changes in direction.
- Example: For a circular path with a radius r, its circumference is given by 2πr. If our runner takes t seconds for one complete round on this track, his speed v is computed as:
v = 2πr / t
(a) A spring expands on application of force;
(b) A spherical rubber ball becomes oblong as we apply force on it.
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Conclusion
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Thus when an object maintains a consistent speed while traveling in a circular path, it is termed uniform circular motion, and its dynamics can be further understood through the equations of motion, as exemplified in the relationship between speed, radius, and time.
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