Скачать или смотреть Shaking Physics Hands With Z Axis Rotation

Per the target.localRotation addition to the code to rotate the target 90 degrees on the Z axis.

// Update is called once per frame
void FixedUpdate()
{
// Position
rb.velocity = (target.position - transform.position) / Time.fixedDeltaTime;

// Rotation

target.localRotation *= Quaternion.Euler(0, 0, 90);

// Calculate the difference between the rotations of the target and the current object
Quaternion roationDifference = target.rotation * Quaternion.Inverse(transform.rotation);

// Convert the rotation difference to an angle and axis representation
roationDifference.ToAngleAxis(out float angleInDegree, out Vector3 rotationAxis);

// Calculate the angular velocity needed to rotate by the rotation difference over a single frame
Vector3 rotationDifferenceInDegree = angleInDegree * rotationAxis;

rb.angularVelocity = (rotationDifferenceInDegree *Mathf.Deg2Rad / Time.fixedDeltaTime);
}