3. explain why a rapidly spinning gyroscope, mounted in a frame that allows it to rotate in any direction independently of the frame’s rotation, tends to maintain its axis pointed in the same direction in space

A wheel or disc like device used for measuring or maintaining orientation and angular velocity in space is known as gyroscope. The wheel or disc rotates freely and can orient in any direction.

Since, there is no external torque acting on the gyroscope, there is no change in the value of the angular momentum. Thus, it maintains direction in which axis points.

i. like it i'm gonna edit it tomorrow

electric field is a function of 1/r^2

yes, the force per unit charge for a point charge is inverse square law.