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).