Inheritance public variables defined in the inspector problem.

So I have this hierarchy.

http://prntscr.com/aq1zwi

What i want to do is have a script associated to Platform like this:

 public class PlatformController : MonoBehaviour {
     
     public float rotationSpeed;
     
     public HandController handController;
 
 }

I want to define these variables in the inspector. Then i have another class for the child objects that extends PlatformController.

 public class RectCenterController : PlatformController
 {
 
     //private variables
 
     void Start()
     {
         //code
     }
 
     void Update()
     {
 
        //code
 }
 }

What i want to do is use PlatformController variables (that I define in the inspector) in RectCenterController but when i declare them as public it makes it so that RectCenterController has to define them in the inspector too, reseting them to the default values (0 and null).

I tried using protected variables in PlatformController, it works, but it doesn't allow me to define handController in the inspector. (It's a variable from the scene.)

HandController is an object from the Leap Motion SDK btw.