When analyzing a rigid body in planar motion, which of the following concepts are essential to consider?
a) Throughout the motion of the rigid body, different points on the body can have different velocity vectors.
b) The angular velocity of the body is the same for all points on the body in plane motion.
c) The velocity of any point on the body is independent of the velocity of its center of mass.
d) The acceleration of a point on a rigid body in plane motion is always in the direction of the net external force acting on that point.