Cant understand Centripital acc

[vuser88]

Hello! I am a 3rd year physics student and i hate the way i have been tought physics all my life. Its always mindless mathematics.. It turns out that i have a hard time understand basic concepts b/c my professors would rather go through derivations covering 4 blackboards then explain what's really happening. So i took it upon myself to go back and re-learn stuff that i should have already mastered.

I was reading a book on nuclear science and eng, mainly fusion ( i don't understand how it works but that's what sparked my question)

When a particle is undergoing a motion in a circular fashion, i know how to show that the accelarion will always be inward, i can do the derivation and show that at any instant the components of the acceleration always point to the origin of the rotation.. but how does one explain this without the mathematics.

 

[K^2]

You don't. Acceleration is a purely mathematical concept based on trajectory and coordinate system choice.

 

[AlephZero]

You can give an "arm-waving" explanation by thinking about the velocity vector.

Supppose you are going round a circle at constant speed. The velocity vector is along the tangent to the circle so there is zero velocity towards the center.

If there was an acceleration in the direction of the tangent, your speed would change, so the tangential acceleration is zero.

If there was no acceleration towards the center, you would just keep moving in a strainght line. The size of the centripetal acceleration (relative to your speed) makes you go round a circle of bigger or smaller radius.

But if you can't (or don't want to ) understand something like this from the math, then you are unlikely to make much real progress in science.

 

[Delta2]

From Newton's 2nd law we can see that a force changes the velocity . It can change the direction or the magnitude of velocity or both.

An intuitive understanding is that a force that it is always perpendicular to velocity will change only the direction of velocity , while a force that has always the same direction with velocity will change only the magnitude of velocity. Try to prove the first from Newton's 2nd law and the fact that the force is always normal to v, that is \mathbf{F}\cdot\mathbf{v}=0

 

[K^2]

You still resort to saying that velocity vector is increasing towards the center, which is absolutely no different than saying \frac{dv}{dt} = - a\hat{r}

And it gets worse if you are working in polar coordinates. Velocity vector is a constant vector in direction of θ. Have fun explaining that one without using \frac{d\hat{\theta}}{dt}

 

[rcgldr]

Rather than focus on the term centripetal, perhaps it would be easier to consider acclerations in the direction of travel versus perpendicular to the direction of travel at a moment in time. The acclerations in the direction of travel change the speed, while accelerations perpendicular to the direction of travel only change the direction.

If the accleration is adjusted so that it's always perpendicular to the direction of travel, and restricted to operate on a plane, you get a curved path that remains on the plane while speed remains constant. In a more general case, if the perpendicular component is allowed to change it's direction and not restricted to a plane, you can end up with all sorts of three dimensional paths where the only constant is the speed, sort of like a "course correction" for a spaceship that doesn't affect it's speed.