# Simple Rotating frame of reference

I have a car moving in straight line with certain time-varying acceleration and there is another car moving in a curvilinear way along some curved path with some time-varying acceleration. The inertial reference frame is say fixed at some point in space. The relative velocity and acceleration at any instant is calculated.

• Why is the relative velocity of the car moving in curved path from the point of view of the car moving in straightline, different from the relative velocity of the car moving in straightline from the point of view of the car moving in the curved path?

I know that in mathematical formulation this will involve the instantaneous angular velocity of the car following the curved path. But that is not very intuitive to me. Is there any way I can understand this situation clearly and more intuitively,i.e., Visualize it.

• It isn't different. The relative velocities are the same from either observer. – CuriousOne Jan 6 '16 at 10:36
• Are you sure? The second car is moving in a curved path so there will be a rotation effect for sure. – archangel89 Jan 6 '16 at 10:37
• The direction of the relative velocity vector will rotate even if you take it between a straight line and one point that doesn't lie on the line. Maybe I don't quite understand, yet, what you are trying to ask. – CuriousOne Jan 6 '16 at 10:42
• What I meant to say is the local coordinate fixed on the second car moving along the curved path is rotating with respect to the centre of rotation. – archangel89 Jan 6 '16 at 11:13
• Yes, but working in a non-inertial system has no consequences on the velocity vector. It will cause fictitious forces to appear, which is why Newton's laws are only valid in inertial systems. The relative velocity is not impacted. – CuriousOne Jan 7 '16 at 0:31