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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.
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 .
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 centripetal acceleration is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with Newton's third law of motion , the body in curved motion exerts an equal and opposite force on the other body.
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The net horizontal force producing the centripetal acceleration is generally separated into components that are respectively in the plane of the superelevated (i.e., banked) track and normal thereto. The component normal to the track acts together with the much larger component of gravitational force normal to the track and is generally ...
At low speeds, the spring provides the centripetal force to the shoes, which move to larger radius as the speed increases and the spring stretches under tension. At higher speeds, when the shoes can't move any further out to increase the spring tension, due to the outer drum, the drum provides some of the centripetal force that keeps the shoes ...
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 = =