Centripetal vs centrifugal force explained
Why centripetal force points inward, what the centrifugal effect really is, and how to pick the right speed form when solving circular motion problems.
The inward force that bends a path
Anything moving in a circle is constantly changing direction, and a change in direction is an acceleration even when the speed is steady. That acceleration always points toward the centre of the circle, so a net inward force must be present to produce it. Remove the force and the object leaves along a straight tangent line, exactly what happens when a string snaps or a car slides off an icy bend. Centripetal simply means centre seeking, and the force is whatever agent happens to supply that inward pull.
Centrifugal force is a frame effect
Riders on a spinning ride feel flung outward, which tempts people to call that push a centrifugal force. In the ground frame there is no outward force at all; the wall of the ride pushes you inward and your body's inertia resists the turn, so you press back against the wall. The outward feeling only appears when you describe the motion from the rotating frame itself, where a fictitious centrifugal term is added to make Newton's laws bookkeep correctly. This calculator works in the ground frame, so it reports the real inward centripetal force and never a centrifugal one.
Choosing linear speed or angular velocity
The two speed inputs describe the same motion in different language. Linear speed v is how fast the object travels along the arc in metres per second, while angular velocity omega is how fast the radius line sweeps in radians per second. They are linked by v = omega times r, so at a radius of 0.5 m a linear speed of 5 m/s is the same as 10 rad/s. Use whichever value your problem gives directly to avoid an extra conversion, and remember that doubling the radius at a fixed omega doubles v and therefore raises the force, whereas doubling the radius at a fixed v lowers the force.
What sets the force in real situations
Because force scales with the square of speed, a modest change in how fast you go has an outsized effect on the inward force required. Doubling the speed around the same curve quadruples the force needed, which is why highway ramps post lower limits and why a faster spin stresses a flywheel far more than intuition suggests. Increasing the radius eases the demand at a fixed speed, so wider turns feel gentler. Reading the acceleration alongside the force helps here, since it isolates the geometry and speed from the mass.