A uniform rod of mass M = 431.0 g and length L = 31.1 cm stands vertically on a horizontal table. It is released from rest to fall.
a) Calculate the angular speed of the rod as it makes an angle 45° with respect to the vertical.
b) Calculate the vertical acceleration of the moving end of the rod as it makes an angle 45° with respect to the vertical (take upward as positive and downward as negative).
c) Calculate the normal force exerted by the table on the rod as it makes an angle 45° with respect to the vertical.
d) If the rod falls onto the table without slipping, find the linear acceleration of the end point of the rod when it hits the table.