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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.
With respect to a coordinate frame whose origin coincides with the body's center of mass for τ() and an inertial frame of reference for F(), they can be expressed in matrix form as:
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
Since the sum of all forces is the centripetal force, drawing centripetal force into a free body diagram is not necessary and usually not recommended. Using F net = F c {\displaystyle F_{\text{net}}=F_{c}} , we can draw free body diagrams to list all the forces acting on an object and then set it equal to F c {\displaystyle F_{c}} .
In classical mechanics, Bertrand's theorem states that among central-force potentials with bound orbits, there are only two types of central-force (radial) scalar potentials with the property that all bound orbits are also closed orbits. [1] [2] The first such potential is an inverse-square central force such as the gravitational or ...
Newton illustrates his formula with three examples. In the first two, the central force is a power law, F(r) = r n−3, so C(r) is proportional to r n. The formula above indicates that the angular motion is multiplied by a factor k = 1/ √ n, so that the apsidal angle α equals 180°/ √ n.
Since the centrifugal force of the parts of the earth, arising from the earth's diurnal motion, which is to the force of gravity as 1 to 289, raises the waters under the equator to a height exceeding that under the poles by 85472 Paris feet, as above, in Prop. XIX., the force of the sun, which we have now shewed to be to the force of gravity as ...
which means the centripetal force is equal to the perturbation in lift force. For the speed, resolving along the trajectory: = where g is the acceleration due to gravity at the Earth's surface. The acceleration along the trajectory is equal to the net x-wise force minus the component of weight.