Solution of the D6 version 67 of Reshebnik on theoretical mechanics manuals SM Targ 1982.
CONDITION TO THE PROBLEM C3 (p. 73-78 in the training manual Targ SM 1982.):
Homogeneous horizontal platform (circular radius R or rectangular with sides and R 2R, where R = 1.2 m) m1 = weight of 24 kg is rotated with an angular velocity ω0 = 10 s-1 around the vertical z axis spaced from the center of mass of the platform on C distance OC = b (Figure D6.0 -D6.9, Table D6..); sizes for all of rectangular platforms are shown in Fig. D6.0a (top view).
At time t0 = 0 the chute platform begins to move (under the influence of internal forces) load D m2 = weight 8 kg law s = AD = F (t) where s is expressed in meters, t - in seconds. At the same time the PA platform, shown in PHC. 0-4, starts to operate a pair of forces with the moment M (given in nyoton-meters, with M <0, its direction is opposite to that shown in the figures); platforms, shown in Fig. 5-9, M = 0.
Define: platforms, shown in Fig. .. 0-4, the relationship ω = f (t), ie, angular velocity platform as a function of time; platforms, shown in Fig. 5-9, - angular speed ω1 platform at time t1 = 1 sec.
The form of the trough in Fig. 0-4 straight (KE trough) in Fig. 5, 6, 7 - a circle of radius R (rim platform) in Fig. 8, 9 - a circle of radius r = 0,5 R, In all the figures shown in the load position D, wherein s> 0 (when s <0, the weight is on the other side of the point A); Fig. 9.5 s = AD distance measured along a circular arc. Playing the drawing of the problem, to hold the z-axis at a predetermined distance OS = L from the center of S.