Centripetal force facts for kids
Centripetal force is an accelerating force that acts on any body that revolves around a centre. This force contributes to keeping the body in rotation. This force is always directed towards the centre.
The opposite force (by Isaac Newton's third law of motion) is called centrifugal force. This is the force that acts on the body in a direction away from the centre, which contributes to making the body try to fly away. When you hold a rope with a heavy object attached to it, and rotate it around, the rope becomes tight and keeps the body from flying away. This is caused by centripetal force.
An example is a roller coaster which uses centripetal force to accelerate the carts so they will keep going in a circular motion. Even if an object changes direction but maintains at a constant speed it still counts as acceleration.
Geometric proof for uniform circular motion
In the figure to the right we define the displacement vector to represent motion in a circle. The magnitude of is denoted as and represents the radius of the particle's orbit.
Images for kids

Polar unit vectors at two times t and t + dt for a particle with trajectory r ( t ); on the left the unit vectors uρ and uθ at the two times are moved so their tails all meet, and are shown to trace an arc of a unit radius circle. Their rotation in time dt is dθ, just the same angle as the rotation of the trajectory r ( t ).

Local coordinate system for planar motion on a curve. Two different positions are shown for distances s and s + ds along the curve. At each position s, unit vector un points along the outward normal to the curve and unit vector ut is tangential to the path. The radius of curvature of the path is ρ as found from the rate of rotation of the tangent to the curve with respect to arc length, and is the radius of the osculating circle at position s. The unit circle on the left shows the rotation of the unit vectors with s.