question_answer 40)

                  Choose the correct alternatives:                 (a) For a general rotational motion, angular momentum L and angular velocity \[\omega \] need not be parallel.                 (b) For a rotational motion about a fixed axis, angular momentum L and angular velocity \[\omega \] are always parallel.                 (c) For a general translational motion momentum p and velocity \[\upsilon \] are always parallel.                 (d) For a general translational motion, acceleration a and velocity \[\upsilon \] are always parallel.                

Answer:

                  (a, c) (a) The wobbly motion of a wheel rotating about an axis inclined at a small angle to the symmetry axis of the wheel represents a situation where \[\vec{L}\] and \[\vec{\omega }\] are not parallel. (b) Fixed axis should pass through CM of the body.                                                         (False) (c) As \[\vec{p}=m\,\vec{\upsilon },\,\vec{p}\] and \[\vec{\upsilon }\] are always parallel. (d) In projectile motion, \[\vec{\upsilon }\] and \[\vec{a}\,\] (i.e., \[\vec{g}\]) are not always parallel.                    (False)