Solution K4-52 (Figure K4.5 condition 2 SM Targ 1989)

A rectangular plate (Figure K4.0 - K4.4) or a circular plate of radius R = 60 cm (Fig. K4.5 - K4.9) rotates about the fixed axis according to the law φ = f1 (t), given in Table. K4. The positive direction of the angle φ is shown in the figures with an arrows arrow. In Fig. 0, 1, 2, 5, 6, the axis of rotation is perpendicular to the plane of the plate and passes through point O (the plate rotates in its plane); in Fig. 3, 4, 7, 8, 9 the axis of rotation OO1 lies in the plane of the plate (the plate rotates in space). On the plate along the straight line BD (Figures 0-4) or along the circle of radius R (Fig. 5-9) the point M moves; the law of its relative motion, that is, the dependence s = AM = f2 (t) (s is expressed in centimeters, t is in seconds), is given in the table separately for Fig. 0-4 and for Fig. 5-9; b and l are given there. In the figures, the point M is shown in the position at which s = AM> 0 (for s <0 the point M is on the other side of point A). Find the absolute velocity and absolute acceleration of the point M at time t1 = 1 s.