FloppyJoint.cs

using UnityEngine;
using System.Collections;

[Script(ScriptRole.View)]
public class FloppyJoint : MonoBehaviour
{
    public float MaxSqrMagnitude; // When the sqrMagnitude of RootVelocity is equal to this number, the angle of the joint is entirely governed by velocity
    public float SnapSpeed; // The speed at which the joint rotates to the target rotation.
    public bool CalculateRestingZ = true; // Whether or not it should calculate Resting Z for joints, if not, the default rotation is used.
    public Transform Parent;

    Transform _parent;
    float _rotationOffset = -90;
    Vector3 _rootVelocity;
    Vector3 _lastFramePosition;
    float _defaultRestingZ;

    void Awake()
    {
        if (Parent == null)
            _parent = transform.parent;
        else
            _parent = Parent;

        // Initialize the _lastFramePosition to the starting position;
        _lastFramePosition = transform.position;

        if (!CalculateRestingZ)
            _defaultRestingZ = transform.eulerAngles.z;
    }

    void UpdateRootVelocity()
    {
        // Keep track of instanaeous velocity.
        _rootVelocity = _lastFramePosition - transform.position;
        _lastFramePosition = transform.position;
    }

    void Update()
    {
        UpdateRootVelocity();

        float restingZEuler;
        var flip = Mathf.Sign(_parent.localScale.x);

        if (CalculateRestingZ)
            restingZEuler = Mathf.Atan2((_parent.transform.position.y - transform.position.y), (_parent.transform.position.x - transform.position.x) * flip) * Mathf.Rad2Deg + _rotationOffset;
        else
            restingZEuler = _defaultRestingZ;

        var velocityZEuler = Mathf.Atan2(-_rootVelocity.y, -_rootVelocity.x * flip) * Mathf.Rad2Deg + _rotationOffset;

        var targetZEuler = Mathf.LerpAngle(restingZEuler, velocityZEuler, _rootVelocity.sqrMagnitude / MaxSqrMagnitude);
        transform.eulerAngles = Vector3.forward * Mathf.LerpAngle(transform.eulerAngles.z, targetZEuler, Time.deltaTime * SnapSpeed);
    }
}