Elementary Plane Rigid Dynamics by H. W. Harkness

By H. W. Harkness

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At what speed will the system turn if the weights are pulled in so as to move in a circle of 1 ft radius? Compare the kinetic energies in the two positions and calculate the work done or the system. 12. ft long is pivoted on a horizontal axis 2 ft from one end and allowed to fall from the horizontal position. Calculate its angular acceleration when it has fallen through 60° and its angular velocity when it reaches the vertical position. 13. A horizontal trap door has a radius of gyration about its line of hinges of 4 ft and its center of gravity is 3 ft from the line of hinges.

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.

II-7 EXAMPLE A 3200-lb vehicle travels round an unbanked track of 300 ft radius at a speed of 30 fps. The center of gravity is 4 ft above the road and the wheels are 5 ft apart. Find the reaction on the wheels. ) Before proceeding to the solution of this problem the reader should satisfy himself that, within the limits of precision of the CM. —a — Fv w FIG. II-8 60 II. GENERAL PLANE MOTION OF A RIGID BODY data supplied, this may be considered a problem in pure translation. M« RD{ = 1360 lb EXAMPLE A railway engine rounds a 600-ft curve at 40 mi/hr.

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