Force exerted by rod on a mass moving in vertical circle

[vcsharp2003]

Tangential acceleration is the component of acceleration parallel to the velocity. If speed is constant, that must be zero.
(In vectors, $0=\frac{d}{dt}v^2=\frac{d}{dt}\vec v^2=\vec v.\dot{\vec v}=||\vec v|| a_t$.)

Yes, I get that part. If only direction of velocity is changing but not it's magnitude then tangential acceleration must be zero.

 

[vcsharp2003]

(In vectors, $0=\frac{d}{dt}v^2=\frac{d}{dt}\vec v^2=\vec v.\dot{\vec v}=||\vec v|| a_t$.)

Why did you take derivative of $v^2$?

 

[haruspex]

Why did you take derivative of $v^2$?

The speed, v, is constant if and only if $v^2$ is constant. Using the squared form let's me write it in vectors easily.
But I did omit a factor 2, now corrected.

 

[vcsharp2003]

The speed, v, is constant if and only if $v^2$ is constant. Using the squared form let's me write it in vectors easily.
But I did omit a factor 2, now corrected.

That's a very nice mathematical way of reasoning it, that I was unaware of. Thankyou for that great tip.