5/7 The rectangular plate is rotating about its corner axis through O with a constant angular velocity = 10 rad/s. Determine the magnitudes of the velocity v and acceleration a of the corner A by (a) using the scalar relations and (b) using the vector relations. 2 400 mm 300 mm 3 (0) B A

2/135 As the hydraulic cylinder rotates around O, the ex- posed length 1 of the piston rod P is controlled by the action of oil pressure in the cylinder. If the cyl- inder rotates at the constant rate 0 = 60 deg/s and 1 is decreasing at the constant rate of 150 mm/s, calculate the magnitudes of the velocity v and ac- celeration a of end B when 1 = 125 mm. Ans. U = 545 mm/s, a = 632 mm/s² 375 mm 0 Problem 2/135 B

For the diagram below the angular velocity of the wheel is w = 2rad/s. The location of the instantaneous center of zero velocity is at point 0.3 m OD 1.2 m OB 45% O somewhere not listed in the other options. OC 0.3 m C

Determine the following: 1. The position vector of point B with respect to point A: rBA = ( i + j + k)m 2. The unit vector in the direction of vector F: u = ( i + j + k) Express your results using three significant figures.

The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity VA = 0.70 m/s to the right, compute the velocity of the center O (positive if to the right, negative if to the left) and the angular velocity w (positive if counterclockwise, negative if clockwise) of the reel. 1.72 m A Answers: Vo = W= 0.60 m 1.075 i 1.25 m/s rad/s

The disk in Figure, rotates about a fixed axis throughO with angular velocity ω =5 rad/sec and angularacceleration α = 3 rad/sec2in the directions shown at acertain instant. The small sphere A moves in the circularslot, and at the same instant, β = 30°, ?̇ = 2rad/sec, and?̈ = - 4 rad/sec2. Determine the absolute velocity andacceleration of A at this instant.

The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity VÀ = 0.84 m/s to the right, compute the velocity of the center O (positive if to the right, negative if to the left) and the angular velocity w (positive if counterclockwise, negative if clockwise) of the reel. Answers: Vo = W = 1.91 m i 0.69 m 1.315 1.37705 Ja m/s VA A rad/s

I need help in solving question three. The items needed to solve three come from the scenario in question 2

A motorcycle cage has a curved path in the x-z plane as shown. The cage path has different curved profile, and between point o and A the path is best described as z = f(x) = ax², where a = 0.09 and b = 1.23. The motorcyclist at point M is moving at a velocity of 12.6 m/s which is increasing at a rate of 1.9 m/s?. If the horizontal position of the motorcyclist at point M is xM = 11.9 m, determine (i) the direction of the motorcyclisť's velocity. (ii) the radius of the curvature of the cage's path at point M, (iii) the normal acceleration at point M, (iv) the magnitude and direction of the motorcyclist's acceleration at point M. A (z = ax

The bent rod rotates about an axis connecting points A and E. All bends in the rod are 90° angles, and the given dimensions are h=21 cm, / = 14.5 cm, d = 21cm, and b = 7.6 cm. Express all your answers using the component system shown. If, at the instant shown, the rod is rotating with a constant angular speed of 26 rad/s and the rotation is counterclockwise as viewed from A looking toward E, determine the velocity and acceleration of point C. (Round the final answers to four decimal places. Include a minus sign if necessary.) The velocity of point Cisc The acceleration of point C is ac = Â) cm/s. k)cm/s²