A particle is found to be at rest when seen from frame S1...

A particle is found to be at rest when seen from frame $S_{1}$ and moving with a constant velocity when seen from another frame $S_{2}$. Mark the possible points from the following : (a) both the frames are inertial (b) both the frames are non-inertial (c) $S_{1}$ is non-inertial and $S_{2}$ is inertial (d) both (a) and (b) are correct

A particle is found to be at rest when seen from frame $S_{1}$ and moving with a constant velocity when seen from another frame $S_{2}$. Mark the possible points from the following :
(a) both the frames are inertial
(b) both the frames are non-inertial
(c) $S_{1}$ is non-inertial and $S_{2}$ is inertial
(d) both (a) and (b) are correct

Key Concepts

Inertial Frame

An inertial frame is a reference frame in which Newton's first law holds and objects not subjected to any net force move in a straight line with constant velocity (or remain at rest). In the context of the problem, if a particle is at rest in one inertial frame and moves with constant velocity in another, the relative motion between the two frames is a uniform translation without acceleration, which is characteristic of inertial frames.

Non-Inertial Frame

A non-inertial frame is a reference frame that is accelerating with respect to an inertial frame, and within such a frame, fictitious forces (like centrifugal or Coriolis forces) must be introduced for Newton's laws to hold. If a particle is observed to be at rest in one non-inertial frame, the presence of these fictitious forces complicates the analysis. In the problem, if one frame were non-inertial, the particle’s observed constant motion in the other frame would not generally be explainable merely by a constant relative velocity, thereby making the non-inertial explanation less consistent.

Relative Motion and Velocity Transformation

Relative motion involves comparing the positions and velocities of objects (or frames) from different reference frames. When two inertial frames move at a constant velocity relative to one another, the transformation of velocities between the frames is straightforward (Galilean transformation in classical mechanics), explaining how a particle at rest in one frame can have a non-zero but constant velocity in the other. This concept is critical in understanding why both frames being inertial is the most natural explanation in this problem.

Transcript

Please give Ace some feedback