How is centripetal force involved here? (charged mass sliding down a conducting hemisphere)

[kuruman]

It can be surprising, though. On the thread about a planet in an elliptical orbit it struck me that the centripetal force is only towards the star at the apogee and perigee. At other points the gravitational attraction has a tangential component.

Sure. This is similar to 2D projectile motion near the surface of the Earth. There is always a centripetal component that becomes equal to the weight at the top of the trajectory.

 

[tellmesomething]

It often happens that there is an analytic way to find velocity as a function of position (e.g. by energy conservation) but not as a function of time. In such cases, the substitution $\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=\frac{dv}{dx}v$ can be useful.

To be exact, the component of that vector sum normal to the velocity is the centripetal force.

I see... Thankyou :)