So I've been trying to implement a 2d top down door that I want to behave like the doors in the game Darkwood but I'm having trouble getting it to feel even remotely right. So there's a few things to note: the player is an AABB and the door is an OBB, I'm using SAT to detect collisions from them and get the minimum translation vector (mtv) and then I use a simple check to get the collisions points, and after that I translate the player:

		CollisionData collided = CheckIfDoorAgentCollided(&door, player);

		std::vector<vec2<float>> collisionPoints;
		if (collided.collided)
		{
			collisionPoints = GetPointsInsideDoor(&door, player);
			player += V2(collided.mtv.x, collided.mtv.y);
		}

So far so good, I should note that the player does not have any acceleration or anything I just instantly move the player by a fixed velocity when a key is pressed (I suspect this might be a problem). Anyway here's the code I'm struggling with:

		float dt = 0.0005f;
		if (collided.collided)
		{
			if (collisionPoints.size() > 0)
			{
				//Apply the force in the opposite way of the minimum translation vector
				vec2<float> force = -collided.mtv * 3500.0f;
				vec2<float> centerOfMass = door.hingePosition;
				vec2<float> momentArm = collisionPoints[0] - centerOfMass;

				float inertia = 10.0f;
				float torque = Cross(momentArm, force);

				door.angularVelocity += door.angularAcceleration * dt;
				door.angularAcceleration += (torque / inertia) * dt;		

				if (door.angularAcceleration > 20.0f)
				{
					door.angularAcceleration = 20.0f;
				}
				if (door.angularAcceleration < -20.0f)
				{
					door.angularAcceleration = -20.0f;
				}
				door.active = true;
			}
		}

		if (door.active)
		{
			//If we're close to 0 we stop
			if (fabsf(door.angularAcceleration) < 0.0000001f)
			{
				door.angularAcceleration = 0.0f;
				door.angularVelocity = 0.0f;
				door.active = false;
			}
			else
			{
				//I think this is where something more sophisticated is needed
				float fakeFriction = -door.angularAcceleration * 0.08f;
				door.angularAcceleration += fakeFriction;
				door.angularVelocity += door.angularAcceleration * dt;
			}
		}

		door.rotationRadians += door.angularVelocity * dt;

		RotateDoorRadians(&door, door.rotationRadians);

Ignoring all those random float values, its just me trying to find a way to make everything seem more natural. Currently getting the door to stop after no force is applied looks very stiff and I can't find the right values for the player to not start sliding along the door which leads me to believe my approach is wrong, here's how it looks:

As you can see it's very stiff and “slidey”, so I was wondering what else I'd need to make the door more realistic? I'd prefer not having to use something like box2d since I'll only need physics for this one thing.