Applied mechanics Volume 1

by Charles Edward Fuller

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 ...Hence the magnitude of the angular velocity will be equal to d6 m w==di, (1) where dO = the angular displacement during the time dt. A distinction should be made between the quantity a, representing the magnitude, or scalar part, of the angular velocity, which we may call angular speed, and the angular velocity, which may be represented by a vector, laid off along an axis perpendicular to the plane of the path of the particle, the direction of the motion being indicated in a manner similar to that in the case of the couple (Art. 64). When the angular velocity is constant, the angular motion of the particle, during the time t, will be equal to 6 = wt (2) When the angular velocity is variable 0 = f wdt, (3) where w = j, (t). If the particle moves in a plane curve and v equals its linear velocity at any point and r = the radius of curvature of the path at that point, its angular velocity about the center of curvature will be equal to dO Ids v-.. w.=di =-rdi=r (4) Transposing we obtain the expression for its linear velocity, da d6,_. v = dl = rw = rdt (5) If the motion is referred to a point O in the plane of the path, which is not the center of curvature, the resultant velocity v may be resolved into a component, dr v1=dt' along the radius vector r, between the point and the particle; and a component d6 = rdt' perpendicular to r. In this case the expression for the resultant linear velocity of the particle may be written Where the quantity Tt may be called the angular velocity of the particle in respect to O. It is evident from the above that, when the second is the unit of time, angular velocity will be expressed in radians per second, which may be abbreviated, rads. per sec. A diagram may be made showing the relation between the angular motion 6 and the time...

94 pages, Paperback

Published May 21, 2012