Download e-book for kindle: Applied Mechanics - Dynamics by Housner G & Hudson D

By Housner G & Hudson D

1950 - utilized Mechanics Dynamics, by way of George W. Housner & Donald E. Hudson (Division of Engineering, California Institute of Technology), D. Van Nostrand Co., Inc., Toronto, N.Y. & London

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7) 30 KINEMATICS : T H E DESCRIPTION O F MOTION The equation of motion is written: where F,, FQ,F, are the components of the resultant force on the particle in the r, 4, z directions, and ( Y - r42), (rd; + 2i4) and f are the components of acceleration. Since the expressions for the acceleration components are not as simple as for rectangular components, it is not desirable to use cylindrical coordinates unless the geometry of the problem is particularly suited to their use. (c) Tangential and normal components are used chiefly because they give a simple representation of acceleration in curvilinear motion.

The vector notation for these quantities will be presented first, and then various scalar components of these vectors will be developed. 1 Displacement, Velocity, and Acceleration. The displacement of a point P (Fig. 1) is described by the magnitude and direction of the radius vector r which extends from the origin of a coordinate system to the point P. At time t let the displacement be r then at time t + At the displacement is r + Ar where Ar is the vector from P to P'. Between P and P' the average change of r per unit time is Ar/At and the velocity at P is obtained by taking the limiting value of Ar/At as At approaches zero: The direction of v is tangent to the path of motion at P.

A rigid straight bar of length 1 slides down a vertical wall and along a horizontal floor as shown in Fig. 11. Find the angular velocity and the angular acceleration of the bar as a function of 8. Solation. 9. A small ring moves on a circular hoop of radius r. A rod OA passes through the ring and rotates about the fixed point 0 on the circumference of the ring with a constant angular velocity 4. Find the absolute acceleration of the ring. 10. A rigid body is rotating with an angular velocity of magnitude 500 rprn about a fixed axis which has the direction and location of the radius vector 3i + 2j - k.

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Applied Mechanics - Dynamics by Housner G & Hudson D


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