A copy of Valve's physics following logic as seen in 'The Lab'

PhysicsFollow.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class PhysicsFollow : MonoBehaviour
{
    public Transform follow;
    public Rigidbody rb;

    void FixedUpdate()
    {
        if (rb == null)
        {
            return;
        }
        
        Vector3 velocityTarget, angularTarget;
        bool success = GetUpdatedAttachedVelocities(follow, out velocityTarget, out angularTarget);
        if (success)
        {
            float maxAngularVelocityChange = MaxAngularVelocityChange;
            float maxVelocityChange = MaxVelocityChange;

            rb.velocity = Vector3.MoveTowards(rb.velocity, velocityTarget, maxVelocityChange);
            rb.angularVelocity = Vector3.MoveTowards(rb.angularVelocity, angularTarget, maxAngularVelocityChange);
        }
    }


    // Magic Numbers
    const float MaxVelocityChange = 10f; /// 10f
    const float velocityMagic = 6000f; /// 6000f
    const float AngularVelocityMagic = 50f; /// 50f
    const float MaxAngularVelocityChange = 20f; /// 20f

    protected bool GetUpdatedAttachedVelocities(Transform target, out Vector3 velocityTarget, out Vector3 angularTarget)
    {
        bool realNumbers = false;

        Vector3 positionDelta = (target.position - transform.position);

        velocityTarget = (positionDelta * velocityMagic * Time.deltaTime);

        if (float.IsNaN(velocityTarget.x) == false && float.IsInfinity(velocityTarget.x) == false)
        {
            realNumbers = true;
        }
        else
        {
            velocityTarget = Vector3.zero;
        }

        Quaternion targetItemRotation = target.rotation;
        Quaternion rotationDelta = targetItemRotation * Quaternion.Inverse(transform.rotation);

        float angle;
        Vector3 axis;
        rotationDelta.ToAngleAxis(out angle, out axis);

        if (angle > 180)
        {
            angle -= 360;
        }

        if (angle != 0 && float.IsNaN(axis.x) == false && float.IsInfinity(axis.x) == false)
        {
            angularTarget = angle * axis * AngularVelocityMagic * Time.deltaTime;
            realNumbers &= true;
        }
        else
        {
            angularTarget = Vector3.zero;
        }

        return realNumbers;
    }
}