Doubt 1 : In the figure shown , a particle is initially placed at (a,0) and then the force F is applied in the direction of negative y axis. I am confused about what will be the torque acting on the particle about the y axis. It seems that it is 0 because the particle is not rotating about the y axis, but mathematically the cross product i x (-j) is not 0 (but the component of torque in the direction of y axis is indeed 0, and that makes me still more confused).
Doubt 2: What is the relation between torque acting on a body about an axis and the body rotating about that axis , i.e , can a body be in rotational motion about an axis only when torque acts on it (and moreover when the torque has non 0 component in the direction of axis), or not. [In Uniform Circular motion(which I think is rotational motion about the symmetric axis perpendicular to the plane) no such torque acts, so is it rotational motion or not]
Doubt 3 : What is the basic definition of AXIS OF ROTATION. Is the statement " axis of rotation is always perpendicular to the plane of rotation" correct?
Also, what is the best definition of Rotational Motion about an axis ?