Velocity and Acceleration in Path Coordinates

Even when a particle draws a planar curved path that is not a circle, it is possible to describe its velocity and acceleration in terms of unit vectors that are tangential and normal to the path. Consider a particle traversing a complex planar curve. Let t be the unit vector tangent to the particle path and let n be the unit normal vector drawn outward as shown in Fig. 2.7b. The velocity and acceleration of particle P can then be written as v = v t = (ds/dt) t (2.10a)

in which s is the arc length along the particle path, v = ds/dt is the speed of the particle, and p is the radius of curvature. it is defined as the radius of the largest circle that has the same tangent with the particle path at point P. In a sense, Eqn. 2.10 can be considered as a generalization of Eqn. 2.9. It is used quite often in the analysis of motion of satellites and stars because of the elliptical nature of their particle path.

Getting Started With Dumbbells

Getting Started With Dumbbells

The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.

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