# Dependence of curved path on frame of reference and force

I was studying projectile motion and suddenly thought that is it possible for particle to move along a circular path without any force acting on it ? (I m not talking about circular motion as it necessarily need centripetal force,you may consider it like a parabolic path). By drawing certain diagrams and assuming the case of a body thrown under no influence of gravity I concluded that it is not possible,but it will be nice to have your comments and advice regarding this concept. Further will our answer be altered by choice of frame of reference chosen to view the particle?

• It is possible if the observer is in a non-inertial frame of reference that is moving in a circular path. Oct 4, 2016 at 12:36

I would give one reason why it would not continue in a circular path:

Inertia will push it off at a tangent.

As regards frames of reference, I can't immediately think of any reason why it would not be viewed as moving in a straight line in any frame.

• can't get the second one Oct 4, 2016 at 1:33
• No offence intended, bit are you asking me to explain the concept of a Lagrangian or is that you follow it but you don't know why I mentioned it here.
– user108787
Oct 4, 2016 at 1:38
• yes the reason why concept of a Lagrangian is mentioned here is unclear to me Oct 4, 2016 at 1:43
• I have deleted the reference as I think it's redundant to analyse such a simple straight line in kinetic energy terms. I also want to check it by writing it explicitly, which as its 3 am here, if you don't mind i will . Leave it till tomorrow :).
– user108787
Oct 4, 2016 at 1:55

Unless Newton's laws of motion are wrong, the answer is clearly "no".

I'm assuming the OP is thinking about Newtonian mechanics, not General Relativity - i.e. I'm considering gravity to be a "force" and not "the intrinsic curvature of space-time caused by the existence of mass."

• who is the OP?? Oct 4, 2016 at 2:47

Well, What do we determine as straight? We perceive something to be 'straight' by comparing it to light, and how our physical receptors receive this light. However, a rod bent at the right angle will appear straight by conventional standards if it is placed the right way in the water (idea from an old docco I watched some months back). Though I understand this concept is in terms of diffraction, there may be some cross over in terms of what we perceive as straight.

But! To the question, if there is no force on an object, it is said to be traveling at a constant velocity. A circular path denotes a change in velocity (vector quantity etc). Which is evidently problemtic in the above problem.

So I cannot see a reason for it either, unless for some odd reason your frame of reference is moving around your stationary object...? In which case it will be PERCEIVED to move in a circular path relative to your frame of reference whilst maintaining constant velocity with all forces in equilibrium.