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 Excerpt: ...one revolution. The speed of a rotating body in radians per second is called the angular velocity or the spin velocity of the body. Consider a particle of the wheel at a distance r from the axis of rotation. As the wheel rotates this particle travels in a circle of which the circumference is 2rr and it travels n times ...
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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 Excerpt: ...one revolution. The speed of a rotating body in radians per second is called the angular velocity or the spin velocity of the body. Consider a particle of the wheel at a distance r from the axis of rotation. As the wheel rotates this particle travels in a circle of which the circumference is 2rr and it travels n times round this circle per second so that the velocity v of the particle is v = 2mr, (2) or using a for 2irn according to equation (1), we have: v = ur (3) If the spin velocity of the wheel is doubled it is evident from this equation that the velocity of every particle in the wheel will be doubled so that the kinetic energy of every particle in the wheel will be quadrupled. Therefore the total kinetic energy, W, of a rotating wheel is quadrupled if the spin velocity a of the wheel is doubled; that is, for a given wheel, W is proportional to Oj2, and for the given wheel there is a definite constant by which w2 may be multiplied to give W. That is: W = Kf (4) where K) is the proportionality factor for the given wheel. The constant K is called the moment of inertia of the wheel, and it depends upon the size, shape, and mass of the wheel. The kinetic energy of a particle is equal to %mv, where m is the mass of the particle in pounds, v is its velocity in feet per second, and kinetic energy is expressed not in foot-pounds, but in foot-poundals. Throughout this discussion of moment of inertia distance is expressed in feet, velocity in feet per second, mass in pounds, force in poundals, torque in poundal-feet, work or energy in foot-poundals, and moment of inertia in pound-feet.2 81. General integral expression for moment of inertia. Imagine a small particle of mass dm to be added to the spinning body at a distance r from the axis of spin. Then the veloci...
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Add this copy of An Elementary Treatise on Calculus to cart. $61.07, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2015 by Palala Press.