# Calculating equatorial velocity

I'm confused about some results I've been getting. I tried calculating the equatorial velocity of Earth by the equation $$R\varpi=v$$, and I got ~465 $$m/s$$. According to various resources, this is correct. But then I tried to calculate it again, using $$g=a_{c}=\frac{v^{2}}{R}$$, and I got ~8000 $$m/s$$.

Obviously, the second is wrong. My question is why? My only guess is that maybe g doesn't work as $$a_{c}$$ in this case due to the normal force from the Earth or something of the sort, but that seems a weak explanation...

It's wrong because the equation is not the correct one to use.
You have calculated the speed an object would have to travel in orbit around the Earth if its path was literally just above the surface. In other words, its centripetal force was provided by its weight.

earth has both rectilinear and rotatory motion.but you take a=v^2/r.so your assumption is wrong.

hi,friend in your equation how we have take a=g.that is for surface on earth and although 'g' is not constant at all.