Centripetal acceleration equation

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SUMMARY

The centripetal acceleration equation, defined as a = V²/r, where V represents speed and r is the radius, effectively describes the acceleration experienced by an object moving in a circular path. The discussion clarifies that while speed remains constant, the velocity changes due to the continuous change in direction, which is the essence of centripetal acceleration. The relationship between speed, radius, and acceleration is intuitive when considering the effects of string length and rotational speed on direction change. Time is inherently included in the equation through the units of speed, measured in meters per second.

PREREQUISITES
  • Understanding of basic physics concepts, particularly motion and acceleration.
  • Familiarity with the definitions of speed and velocity.
  • Knowledge of circular motion dynamics.
  • Basic mathematical skills for manipulating equations.
NEXT STEPS
  • Study the relationship between speed and acceleration in circular motion.
  • Explore the concept of angular velocity and its impact on centripetal acceleration.
  • Learn about the effects of radius on acceleration in circular paths.
  • Investigate real-world applications of centripetal acceleration in engineering and physics.
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Students of physics, educators teaching circular motion, and anyone interested in understanding the principles of acceleration in rotational systems.

johndb
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I find the equation for centripetal acceleration non-intuititive. V^2/r tells me velocity is multiplied by the velocity ( which at this stage is usually a very large number) then this is divided by the radius.. Leaves me with subdivisions that happen to equal the rate of acceleration..Dubious.. And why like in linear acceleration is there no recognition of initial and final velocities and even a dimension of time. Is anyone else discomforted by this and can anyone shed some light on this, thanks.
 
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The v in the equation is not velocity, it's speed. Even if this speed is constant, the velocity is constantly changing because the direction is constantly changing. It is this change in direction (in the case of constant speed) that constitutes the acceleration.

In that light, the situation is perfectly reasonable and intuitive. The faster you swing a weight on the end of a string, the more quickly it is changing direction, so the higher the acceleration. The longer the string, the slower the change in direction (at the same speed) and therefore the lower the acceleration

And time is in the equation, in v (as meters per second, for example).
 

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