Centripetal Force
Spin an object in a circle and watch the interplay of velocity, centripetal acceleration, and tension. Release the string to see Newton’s first law in action—the object flies off along the tangent, not outward.
Click Release or press Space to let go of the string and watch the object fly off tangentially. Use R to reset. Switch scenarios to see how centripetal force works differently in each context.
Centripetal vs. Centrifugal
When an object moves in a circle, it is constantly accelerating toward the center—this inward acceleration requires a real force called centripetal force. The word comes from Latin: centrum (center) + petere (to seek). It is not a new kind of force but rather a role played by tension, gravity, friction, or normal force depending on the scenario.
Centrifugal force is what you feel pushing you outward on a merry-go-round, but it is a fictitious force—an artifact of observing from a rotating reference frame. In the inertial frame, your body simply wants to travel in a straight line (Newton’s first law), and the seat pushes you inward. There is no outward force; only inertia resisting the change in direction.
The math
For uniform circular motion the centripetal acceleration is a = v²/r = ω²r,
and the required force is F = mv²/r = mω²r. The velocity vector is always
tangent to the circle and perpendicular to the radius.
Why Objects Fly Off Tangentially
When you release the string, the centripetal force vanishes. With no force acting on it (ignoring gravity for the moment), the object obeys Newton’s first law: it continues in a straight line along its instantaneous velocity vector, which is tangent to the circle at the point of release. It does not fly radially outward, despite what intuition might suggest.
This is exactly why a hammer thrower releases at a specific angle—the hammer departs along the tangent, not directly away from the athlete. Try releasing at different points in the simulation to see how the departure angle changes.
Banked Curves and Orbits
On a banked curve, the road is tilted so that a component of the normal force
provides the centripetal force, reducing or eliminating the need for friction. At the
ideal banking angle θ = arctan(v²/rg), a car can navigate the curve
on pure ice without sliding.
For a satellite in orbit, gravity provides all of the centripetal force. Setting
GMm/r² = mv²/r gives the orbital velocity v = √(GM/r).
Higher orbits are slower; lower orbits are faster. In the loop-the-loop scenario,
at the top of the loop both gravity and the normal force point inward, requiring a minimum
speed of v = √(gr) to maintain contact.