Q4. The member OA of the industrial robot can rotate about the fixed point O and also change in length -- that is, distance between O and A can increase or decrease. At the instant shown, 0 = 60 degrees, è = 1.2 rad/s, and = 0.8 rad/s². Let us denote the distance OA by the variable r. We are told that r = 0.9 m, i = 0.5 m/s, and i = -6 m/s?. All motion is restricted to the x-y plane. a) Represent the velocity and acceleration of point A as vectors in terms of polar coordinates. i.e., write v = (some number) e, + (some number) ee. Do the same for acceleration vector a as well. %3D

Calculate the position of the centroid. Use the axes of the figure. It is possible to make the calculation from three geometric shapes only. Answer: Xc = 16.4 cm Yc= 6.5 cm

The stars Rigel, Betelgeuse and Aldebaran make up the asterism (unofficial star pattern) known as the winter triangle. Assuming that you have taken a look at each of these stars, including the moon, in this order: Rigel – Betelgeuse – Aldebaran – Moon, what would be the resultant vector, that is, the displacement between Rigel and the Moon. Each tick (the little lines) of the ruler corresponds to one unit. Find the distance between each vector points, their angles, and find the resultant vector. Illustrate a graph showing the proper labeling of the vectors (e.g. Rigel – Betelgeuse is ), the angle of each vector and the magnitude and angle of the resultant vector. (Please include a detailed and complete solution) Refer to this image:

A right triangle with sides of 3, 4, and 5 units has angles that are 37°, 53°, and 90°, respec- tively. Which of its sides is the hypotenuse? Which side is opposite the 37° angle? Which side is opposite the 53° angle?