You're going to open the door further by giving it a brief, hard push. first, you'll push the door at its center. then, you'll push it near the door knob. both pushes are equally hard, and last the same length of time. and in both cases you direct your push perpendicular to the plane of the door. (a)which push will give the door more rotational motion?

The closer you are to the hinge, the harder it is to rotate the door.

Just like translational motion depends on the force applied, rotational motion depends on the torque applied.
Torque mathematically is = F x r ; here the 'x' signifies cross multiplication between the vectors and r is the radius of the rotation body

We can see, with the same force, more the radius, more the torque and thus more rotational motion.

Rain is pulled by gravity which is a non contact force