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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.
are called the tangential acceleration and the normal or radial acceleration (or centripetal acceleration in circular motion, see also circular motion and centripetal force), respectively. Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by the Frenet–Serret formulas ...
This acceleration is known as centripetal acceleration. For a path of radius r , when an angle θ is swept out, the distance traveled on the periphery of the orbit is s = rθ . Therefore, the speed of travel around the orbit is v = r d θ d t = r ω , {\displaystyle v=r{\frac {d\theta }{dt}}=r\omega ,} where the angular rate of rotation is ω .
Newton coined the term "centripetal force" (vis centripeta) in his discussions of gravity in his De motu corporum in gyrum, a 1684 manuscript which he sent to Edmond Halley. [ 4 ] Gottfried Leibniz as part of his " solar vortex theory " conceived of centrifugal force as a real outward force which is induced by the circulation of the body upon ...
The acceleration is directed inward, toward the axis of rotation. It points opposite to the position vector and perpendicular to the velocity vector. This inward-directed acceleration is called centripetal acceleration.
Transverse acceleration (perpendicular to velocity) causes a change in direction. If it is constant in magnitude and changing in direction with the velocity, circular motion ensues. Taking two derivatives of the particle's coordinates concerning time gives the centripetal acceleration = =
The centripetal acceleration given by v 2 / r is normal to the arc and inward. When the particle passes the connection of pieces, it experiences a jump-discontinuity in acceleration given by v 2 / r , and it undergoes a jerk that can be modeled by a Dirac delta, scaled to the jump-discontinuity.
The expression on the right hand side is the centripetal acceleration multiplied by mass, the force required to turn the vehicle. The left hand side is the maximum frictional force, which equals the coefficient of friction multiplied by the normal force. Rearranging the maximum cornering speed is