Question

A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod. relative to the positive direction of the axis of rotation, the angular positions of the sphere are positive, its angular velocity is positive, and its angular acceleration is negative. the sphere is
a.rotating clockwise and speeding up.
b.rotating clockwise and slowing down
c.rotating counterclockwise and speeding up
d.rotating counterclockwise and slowing down.
e.first rotating clockwise and then counterclockwise. ? a solid ylinder shown rotates about a fixed axis perpendicular to

Answer 1

d.rotating counterclockwise and slowing down This is a matter of understanding the notation and conventions of angular rotations. Positive rotations are counter clockwise and negative rotations are clockwise. An easy way to remember this is the "right hand rule". Make a closed fist with your right hand and have the thumb sticking outwards. If you orient your thumb such that it's pointing in the direction of the positive value along the axis, your fingers will be curled in the positive rotational direction. So in the described scenario, the sphere is rotating in the positive direction (counter clockwise) and decelerating due to the negative angular acceleration. That immediately indicates that options "a", "b", and "e" are wrong since they mention the sphere going clockwise at the beginning. Of the two remaining options "c" and "d", we can discard option "c" since it has the rotation speeding up, and that leaves us with option "d" where the sphere is rotating counter clockwise and slowing down.