K3 Option 67 (Fig. 6, condition. 7) Targ 1988

Solution to problem K3 Option 67 on theoretical mechanics from the training manual Targ S.М. 1988. Condition for the problem Kinematics No. 2 (p. 26 in the training manual Targ S.M.): A rectangular plate (Fig. K3.0-K3.5) or a round plate with a radius of R = 60 cm (Fig. K3.6 -K3.9) rotates around a fixed axis with a constant angular velocity "omega" specified in table K3 (with a minus sign the direction "omega" is opposite to that shown in the figure). The axis of rotation in fig. K3.0-K3.3 and K3.8, K3.9 are perpendicular to the plane of the plate and passes through point O (the plate rotates in its plane); in fig. K3.4-K3.7 the axis of rotation of OO1 lies in the plane of the plate (the plate rotates in space). A point M moves along the plate along the straight line BD (Fig. K3.0-K3.5) or along a circle of radius R, i.e., along the rim of the plate (Fig. K3.6-K3.9). The law of its relative motion, expressed by the equation s = AM = f (t) (s - in centimeters, t - in seconds), is given in table. K№ separately for fig. K3.0-K3.5 and for fig. K3.6-K3.9, while in Fig. 6-9 s = AM and is counted along an arc of a circle; dimensions b and l are also given there. In all the figures, point M is shown in the position at which s = AM> 0 (for s <0, point M is on the other side of point A). Determine the absolute speed and absolute acceleration of point M at time t1 = 1 s.
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