NO particle can follow a curved path if there is no external force .
this is a newton law -particle move in a straight line untill an extenal force act on it .
so for a curved path external force is necessary.
if there is no force then particle remain at rest or move in a straight line.

 
						

							
Actually particle CAN move without applying force depending on your frame of reference. Though we still use “pseudo-force” or ficticious forces to balance out the motion. Accelerated frames of references usually tend to originate pseudo forces.
Like the rctilinear accelerated frame , rotationally accelerated frame which gives rise to coriolis force and one is euler force which is cause by variable rate of rotation.
In quantum mechanics gravity is also termed as pseudo force since the force exerted by gravity is now believed to be just the “bend” in space which very much explains blackholes.
If u remember few days ago scientists were able to “detect” gravitational waves by detecting the bend in space by measuring the time it takes light to travel to and fro from a certain distance.
Hit me up if any doubt.