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A centripetal force (from Latin centrum, "center" and petere, "to seek" [1]) is a force that makes a body follow a curved path.The direction of the centripetal force is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path.
Unlike tangential acceleration, centripetal acceleration is present in both uniform and non-uniform circular motion. This diagram shows the normal force (n) pointing in other directions rather than opposite to the weight force. In non-uniform circular motion, the normal force does not always point to the opposite direction of weight.
Newton's law of motion for a particle of mass m written in vector form is: = , where F is the vector sum of the physical forces applied to the particle and a is the absolute acceleration (that is, acceleration in an inertial frame) of the particle, given by: = , where r is the position vector of the particle (not to be confused with radius, as ...
A vector field defines a direction and magnitude at each point in space. A field line is an integral curve for that vector field and may be constructed by starting at a point and tracing a line through space that follows the direction of the vector field, by making the field line tangent to the field vector at each point.
In accordance with Newton's first law of motion, an object moves in a straight line in the absence of a net force acting on the object. A curved path ensues when a force that is orthogonal to the object's motion acts on it; this force is often called a centripetal force , as it is directed toward the center of curvature of the path.
For example, consider a path along an arc of radius r, which tangentially connects to a straight line. The whole path is continuous, and its pieces are smooth. Now assume a point particle moves with constant speed along this path, so its tangential acceleration is zero. The centripetal acceleration given by v 2 / r is
A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such ...
The acceleration vector of the parcel is decomposed in the tangential acceleration parallel to s and in the centripetal acceleration along positive n. The tangential acceleration only changes the speed V and is equal to DV/Dt, where big d's denote the material derivative.