Download e-book for iPad: Hungarian problem book I: Based on the Eotvos competitions by E. Rapaport

By E. Rapaport

ISBN-10: 0883856115

ISBN-13: 9780883856116

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Extra info for Hungarian problem book I: Based on the Eotvos competitions 1894-1905

Sample text

This leads to confusion in the use of the general torque equation for plane motion. The working rule, then, for writing the equation for the total torque round any arbitrarily chosen point A is: Note the inertial forces MxA and MyA acting at the chosen point A. Imagine these to be acting at the center of mass, G. Now write the sum of the torques round A including in this sum the torques due to the inertial forces, assumed acting at G. N o t e on the Inertial Forces T h e terms MxA and MyA , or X and Y as here used, have the dimensions of forces but they are not external forces in the Newtonian sense.

Some portion of this external force must be transmitted to the particle w^ (else particle m^ would not be accelerated). Let the part of the force transmitted to mz- be (Xi + Qx) and (F,· + Qy) where X{ and Y2 are the unbalanced portions of the components, respectively, in the X- and Ydirections. The forces Q are stress forces and when we add the forces throughout the whole body these will necessarily disappear in pairs, action and reaction. 38 GENERAL PLANE MOTION OF A RIGID BODY FIG. 39 IM We may now write the simple particle equations of motion for the sample point-mass mt: *.

The wheels have a radius of 24 in. CHAPTER T W O The General Plane Motion of a Rigid Body The General Plane Motion of a Rigid Body Thus far we have considered only special cases of rigid body motion, a body rotating about a fixed axis or about an instantaneous center. We wish to extend our thinking to include bodies which are executing any sort of plane motion. We now think of a body, free to move in a plane, and with a system of plane forces acting upon it. We know from experience that such a body will, in general, be given a rotation as well as a translation.

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Hungarian problem book I: Based on the Eotvos competitions 1894-1905 by E. Rapaport

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