Adding a HingeJoint component

StickOnContact.cs

using UnityEngine;
using System.Collections;

public class StickOnContact : MonoBehaviour
{
	public Collider m_Contactor;

	void OnCollisionEnter(Collision collisionInfo)
	{
		foreach(ContactPoint contact in collisionInfo.contacts)
		{
			if(contact.thisCollider == m_Contactor)
			{
				HingeJoint hingeJoint = gameObject.AddComponent<HingeJoint>();
				hingeJoint.connectedBody = contact.otherCollider.attachedRigidbody;	// OK if it's null
				hingeJoint.axis = Vector3.right;
				hingeJoint.anchor = Vector3.down * 0.6f;

				JointLimits limits = hingeJoint.limits;
				limits.min = -5;
				limits.minBounce = 0;
				limits.max = 5;
				limits.maxBounce = 0;

				hingeJoint.limits = limits;
				hingeJoint.useLimits = true;
				break;
			}
		}
	}
}