Centripetal acceleration

Centripetal Acceleration. Centripetal acceleration, /r or CO r, where is the tangential linear velocity (m/s), rthe radius (m), and CO the angular velocity (rad/s), is, like any other linear acceleration, measured in SI units m/s. Centripetal force, equal to mass times centripetal acceleration, is, like any force in SI, measured in newtons. 

In this case, acceleration represents a change in the direction of the velocity vector, while the magnitude v remains constant. Using the right-hand rule, the acceleration is seen to be directed toward the center of the circle. This is known as centripetal acceleration, centripetal meaning center seeking. The magnitude of the centripetal acceleration is... 

The source is brought to a. positive poteptial (I/) of several kilovolts and the ions are extracted by a plate at ground potential. They acquire kinetic energy and thus velocity according to their mass and charge. They enter a magnetic field whose direction is perpendicular to their trajectory. Under the effect of the field, Bg, the trajectory is curved by Lorentz forces that produce a centripetal acceleration perpendicular to both the field and the velocity. 

Centripetal and Centrifugal Acceleration A centripetal body force is required to sustain a body of mass moving along a curve tra-jec tory. The force acts perpendicular to the direction of motion and is directed radially inward. The centripetal acceleration, which follows the same direction as the force, is given by the kinematic relationship ... 

Equations (2.24 and 2.27) look like as Clairaut s formulas which will be derived later. However, this similarity is superficial, since the former do not contain the flattening of the earth. A variation of the field magnitude, g with latitude. Equation (2.24), is caused by only a change of the centripetal acceleration on the spherical surface. 

The terminal settling velocity u, for a single spherical particle in a centrifugal separator can be calculated from equation 9.5 with the centripetal acceleration rto2 replacing the gravitational acceleration g to give... 

The first of these expresses the condition that the centripetal constraint force does no work, because the velocity is perpendicular to the radius. The second states that the radial component of the acceleration is directed inwards and equal to the square of the speed. This relation can be used to calculate the constraint force by taking the scalar product of the equation of motion (2) with the vector function r[t], and using the constraint and its time derivatives to obtain... 

Besides pumping, centripetal acceleration is created. A maximum fluid rotational velocity of up to 12 m/s, and a corresponding radial acceleration in excess of 106 g have been produced within a diamond-shaped microchamber (55 x 55 im). This notch chamber was constmcted along the side wall of an otherwise straight channel (30 pm wide, 30 pm deep) which was fabricated on a PDMS chip. This microstructure caused flow detachment at the opening of the notch, leading to recirculating flow of microvortex inside the notch [384]. 

Packed bed columns for CEO can also be obtained by using centripetal forces [49,141], Packing of the particles is obtained by centripetal acceleration through the capillary column. The velocity of the particles is given by the sedimentation velocity (used) as follows [49] ... 

While chemical engineers are well-grounded in the mechanics of Newtonian fluids, it is the non-Newtonian character of polymers that controls their processing. Three striking examples [6] of the differences between Newtonian and typical polymeric liquids (either melts or concentrated solutions) are shown schematically in Fig. 1. The upper portion of the figure refers to the Weissenberg effect [7], or rod-climbing, exhibited by polymers excellent photos may be found in Bird et al. [4] as well. When a rod is rotated in a Newtonian fluid, a vortex develops near the rod due to centripetal acceleration of the fluid. When the same experiment is repeated with a polymeric fluid, however, the fluid climbs the rod. In the center... 

Equating the radial components of the forces acting on an electron at A to the centripetal acceleration, multiplying by a2, and substituting the value of Nf from equation 7, we get the equation... 

In circular motion velocity is always parallel to the direction of motion and perpendicular to the radius of motion. The acceleration required to change the velocity s direction, called centripetal acceleration, is always perpendicular to the velocity and toward the center of motion. To change the velocity s magnitude an acceleration is required in the direction of the velocity. Hence, acceleration is required to change both magnitude and direction of velocity and are in different directions. This is applicable to curvilinear motion in general. 

Much of Newton s work involved rotational motion, particularly circular motion. The velocity s direction constantly changes, requiring a centripetal acceleration. This centripetal acceleration requires a net force, the centripetal force, acting toward the center of motion. Centripetal acceleration is given by a(central)=v /R where v is the velocity s magnitude and R is the radius of the motion. Hence, the centripetal force F(central) = mv /R, where m is the mass. These relationships hold for any case of circular motion and furnish the basis for thrills experienced on many amusement park rides such as ferris wheels, loop-the-loops, merry-go-rounds, and any other means for changing your direction rather suddenly. Some particular examples follow. 

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