Centripetal acceleration equation

[johndb]

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.

 

[sethz]

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).

 

[astrokreng]

I can understand your discomfort with the equation for centripetal acceleration. While it may seem non-intuitive at first glance, it is actually a result of the fundamental principles of circular motion.

First, let's break down the equation V^2/r. This represents the velocity (V) of an object moving in a circular path, squared, divided by the radius (r) of that path. This ratio is then multiplied by a constant value, which is the acceleration due to gravity (g).

The reason for squaring the velocity is because circular motion involves constant changes in direction, which can be represented by a vector quantity. Squaring the velocity allows us to work with only the magnitude of the velocity, without worrying about its direction. This is similar to how we use the distance formula (d = rt) in linear motion, where the speed (r) is squared to remove the direction component.

Now, let's consider the absence of initial and final velocities and time in the equation. This is because centripetal acceleration is a measure of the rate at which an object is changing its direction, not its speed. In linear acceleration, we measure the change in speed over a certain amount of time. But in circular motion, the speed may remain constant, while the direction changes. Therefore, time is not a factor in the equation. Additionally, the initial and final velocities are not relevant because the acceleration is constantly changing as the object moves along its circular path.

I hope this explanation sheds some light on the equation for centripetal acceleration. While it may seem counterintuitive, it is a result of the fundamental principles of circular motion. If you have any further questions or concerns, please don't hesitate to ask. As scientists, we are always striving to better understand and explain the world around us.