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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 .
The net acceleration is directed towards the interior of the circle (but does not pass through its center). The net acceleration may be resolved into two components: tangential acceleration and centripetal acceleration. Unlike tangential acceleration, centripetal acceleration is present in both uniform and non-uniform circular motion.
The tangential acceleration only changes the speed V and is equal to DV/Dt, where big d's denote the material derivative. The centripetal acceleration always points towards the centre of curvature O and only changes the direction s of the forward displacement while the parcel moves on.
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With cylindrical co-ordinates which are described as î and j, the motion is best described in polar form with components that resemble polar vectors.As with planar motion, the velocity is always tangential to the curve, but in this form acceleration consist of different intermediate components that can now run along the radius and its normal vector.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
In classical mechanics, the Euler force is the fictitious tangential force [1] that appears when a non-uniformly rotating reference frame is used for analysis of motion and there is variation in the angular velocity of the reference frame's axes.
The formula for the acceleration A P can now be obtained as: = ˙ + + (), or = / + / +, where α is the angular acceleration vector obtained from the derivative of the angular velocity vector; / =, is the relative position vector (the position of P relative to the origin O of the moving frame M); and = ¨ is the acceleration of the origin of ...