The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part Ii. of a Treatise On the Whole Subject, With Numerous Examples
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In our eReader you can find the full English version of the book. Read The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part Ii. of a Treatise On the Whole Subject, With Numerous Examples Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part Ii. of a Treatise On the Whole Subject, With Numerous Examples
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Chap, iv.) also ceases to be limiting friction and becomes only of sufScient magni- tude to keep the point of contact at rest. If sliding ever does cease, we then have u— a(o^= 0, V -l-aa)i =0 (4).
ART. 238.] SPHERE ON AN IMPERFECTLY ROUGH PLANE. 159 The equations (3) and (4) suffice to determine these final values of u, V, fOi and w^. Thus the direction of the motion and the velocity of the centre of gravity after sliding has ceased have been found in terms of the time. It appears that both th...ese elements are independent of the friction.
If the equations (4) hold initially the sphere will begin to move without sliding provided the friction found from the equations (1), (2) and (4) is less than the limiting friction. To determine this point we must find the magnitude of the friction necessary to prevent sliding. If the sphere does not slide we may differentiate the equations (4) ; then substituting from (1) and (2) we find ^'=0 and F=gsiD.a. k^/(a^ + k^). But, since the pressure on the plane is g cos a, this requires that the coefficient of friction fi > tan a -.
What to read after The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part Ii. of a Treatise On the Whole Subject, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Edward John Routh to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Chap, iv.) also ceases to be limiting friction and becomes only of sufScient magni- tude to keep the point of contact at rest. If sliding ever does cease, we then have u— a(o^= 0, V -l-aa)i =0 (4).
ART. 238.] SPHERE ON AN IMPERFECTLY ROUGH PLANE. 159 The equations (3) and (4) suffice to determine these final values of u, V, fOi and w^. Thus the direction of the motion and the velocity of the centre of gravity after sliding has ceased have been found in terms of the time. It appears that both th...ese elements are independent of the friction.
If the equations (4) hold initially the sphere will begin to move without sliding provided the friction found from the equations (1), (2) and (4) is less than the limiting friction. To determine this point we must find the magnitude of the friction necessary to prevent sliding. If the sphere does not slide we may differentiate the equations (4) ; then substituting from (1) and (2) we find ^'=0 and F=gsiD.a. k^/(a^ + k^). But, since the pressure on the plane is g cos a, this requires that the coefficient of friction fi > tan a -.
What to read after The Advanced Part of a Treatise On the Dynamics of a System of Rigid Bodies : Being Part Ii. of a Treatise On the Whole Subject, With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Edward John Routh to read onlineMoreLess
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