dear sir/madam,i had this doubt for quite sometime now,\"what are inertial and non-inertial frames?\" and could you please explain them with proper examples?

an inertial frame of reference is reference frames with the property that every physical law takes the same form in each such frame. In simple words, in inertial frame Newton's law is valid ie. the motion of a particle not subject to forces is in a straight line at constant speed. An inertial frame only can move with constant speed w.r.t some fixed stars (or any object at absolute rest), it can not have accelaration or rotation. Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly ie., in a straight line and at constant speed.

In a very simple language, a non-inertial frame of reference is a reference frame that is not an inertial reference frame. The laws of physics in such a frame do not take on their most simple form. To explain the motion of bodies entirely within the viewpoint of non-inertial reference frames, fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) must be introduced to account for the observed motion, such as the Coriolis force or the centrifugal force, as derived from the acceleration of the non-inertial frame.

In an inertial frame, Newton's second law for a particle takes the form: F = ma

with F the net force , m the mass of a particle and a the acceleration of the particle which would be measured by an observer at rest in the frame.

In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form: F'= ma

where F' = F - 2m(Ωxv) - m Ωx(Ωxr) -mΩ' x r

v and r are the velocity and position of the body and Ω' denotes the derivative of Ω w.r.t time. In the above expression F is same as the force measured in inertial frame. The extra terms are the "fictitious" forces for this frame (The first extra term is the Coriolis force, the second the centrifugal force, and the third the Euler force.). If we consider Ω=0 ie. frame is not rotating or in other words frame is of ineretial frame type then all those extra temrs becomes zero and its simple form F' = F.

thanks for the answer