How to move an object in a circle using rigidbody?

Question

Physics

Hello!
There was such problem: I do particle simulation, and it is necessary for me that on mouse click the particle if it is in the set radius, began to rotate around the mouse pointer. I found a solution where movement happens by changing transform.position:

if (Input.GetMouseButton (1)) {
      timer += Time.deltaTime;
      transform.position = new Vector3 (2*Mathf.Cos(Mathf.Deg2Rad*timer), 2*Mathf.Sin(Mathf.Deg2Rad*timer), 0);
    }

But this solution does not suit me, because, firstly, other forces could act on the particle before the click, and I need it to move taking into account these forces, and secondly, so that it retains energy after the user releases the mouse.
It would be ideal to do this through AddForce.
It should be added that all the action takes place in a two-dimensional plane.
I would be grateful if you could help me write the code!

Answer 1

First drag the particle towards the mouse, and when it is close enough, drag it along the tangent of the desired orbit.

var toMouse = mousePosition - rigidbody.position;
if (toMouse.sqrMagnitude > sqrRadius)
{
    rigidbody.AddForce(toMouse);
}
else
{
    var velocity = rigidbody.velocity;
    Vector3.OrthoNormalize(ref toMouse, ref velocity);
    rigidbody.AddForce(velocity);
}

Vector3.OrthoNormalize will give you the direction of the tangent, you may need to specify a binormal.