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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.
A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame. [1] Fictitious forces are invoked to maintain the validity and thus use of Newton's second law of motion, in frames of reference which are not inertial. [2]
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments ) acting on the rigid body.
A particular solution to Hamilton's equations is called a phase path, a particular curve (q(t),p(t)) subject to the required initial conditions. The set of all phase paths, the general solution to the differential equations, is the phase portrait:
The inward acceleration is 1 metre per square second, v 2 /r. It is subject to a centripetal force of 1 kilogram metre per square second, which is 1 newton. The momentum of the body is 1 kg·m·s −1. The moment of inertia is 1 kg·m 2. The angular momentum is 1 kg·m 2 ·s −1. The kinetic energy is 0.5 joule.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
Then in accordance with Newton's third law of motion, there will also be an equal and opposite force exerted by the object on some other object, [1] [2] and this reaction force is sometimes called a reactive centrifugal force, as it is directed in the opposite direction of the centripetal force.
In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.