Centripetal force thought experiment Suppose I hit a puck on horizontally (tangential to the surface) on a completely frictionless and spherical globe. Since the gravitational and normal contact force cancel eachother out, the net force should be 0 and the puck should move in a straight line with uniform velocity. But if it does, the normal contact force would disappear instantly, leaving behind the radially inward gravitational force which would prevent it from flying off tangentially. So, if im not mistaken, the puck would essentially stick to the surface and circle the earth with constant speed.
But that means that the puck has a centripetal acceleration with an effectively 0 net force. What am i missing here?
P.s to simplify things, there is no air resistance and the planet itself is stationary.
 A: There is no paradox:  the net force is effectively zero, while being non-zero just enough to supply the requires centripetal acceleration.
For an object, mass $m$, to travel at a velocity $v$ in a circle of radius $r$, a centripetal force $F_c$ is required:$$F_c = \frac{m v^2}{r}$$In this case, the velocity is, say, $40 \text{ m/s}^2$ (a $144 \text{ km/hr}$ slapshot), while the radius of the earth is approximately $6.36  \times  10^6$ metres.
Substituting these values and assuming a $1$ kg puck, we get:$$F_c = \frac{1 \times40^2}{6.36  \times  10^6}=2.52\times10^{-4}\text{ Newtons}$$as the required centripetal force.
So a gravitational force of $9.81$ Newtons is almost balanced by a normal force of just slightly less ($25$ parts per million), leaving this tiny centripetal force required.
A: Re, "Since the gravitational and normal contact force cancel each other out..." Contact force doesn't "balance out gravity." It balances out whatever force is trying to push the two solid objects toward each other. When the puck is stationary, then it's just contact force vs. gravity. But if the puck is circling the Earth, then gravity will be "balanced out" by a combination of contact force and the puck's inertia. The faster the puck travels, the more of its weight is supported by its inertia. If it circles the Earth at orbital speed, then the contact force's share will be zero, and the puck's weight will be "balanced" entirely by its inertia.
A: Centripetal forces are not special forces. They do not exist on their own. Forces that exist in a problem can act as centripetal forces.
For example, if you consider a stone tied to a string and swung about in a circle parallel to the ground, then the tension in the string acts as the centripetal force. If you consider a satellite moving in a circular orbit around the earth, the gravitational force acts as the centripetal force there.
In this case, the centripetal force is the vector sum of the gravitational force and the normal reaction. It's important to note that a body does not move in the direction of the net force applied on it. A body moves in the direction of its (resultant) velocity. In your example, the direction of the velocity is changing continuously. The centripetal force in this case, is constant in magnitude and varying in direction (since the gravitational force and the normal reaction are both constant). If you hit the puck with a certain velocity and there were no forces on it at all, then it would leave the surface of the earth. But the reason it keeps changing direction (and therefore continuously maintains contact) is because there is a force in the radial direction. This acceleration causes some velocity to develop in this direction. The puck then moves in the direction of it's resultant velocity. This direction keeps changing at every instant such that it always maintains contact with the surface of the earth.
