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2)A planet orbits a star, in a year of length 4.57 x 107 s, in a nearly circular orbit of radius 1.56 x 1011 m. With respect to the star, determine (a) the angular speed of the planet, (b) the tangential speed of the planet, and (c) the magnitude and direction of the planet's centripetal acceleration.

3)A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner, as the drawing shows. The centripetal acceleration measured at corner A is n times as great as that measured at corner B. What is the ratio L1/L2 of the lengths of the sides of the rectangle when n = 1.66?

4)A star has a mass of 1.81 x 1030 kg and is moving in a circular orbit about the center of its galaxy. The radius of the orbit is 3.1 x 104 light-years (1 light-year = 9.5 x 1015 m), and the angular speed of the star is 2.5 x 10-15 rad/s. (a) Determine the tangential speed of the star. (b) What is the magnitude of the net force that acts on the star to keep it moving around the center of the galaxy?

All help is appreciated, thank you