Physics

Physics

Problem

During a lab, the positive rotational direction is initially defined as clockwise. Just before the sign convention is changed, a disk has an angular velocity of +4 rad/s+4\,\text{rad/s} under that original convention. Immediately after switching to the more common convention that takes counterclockwise as positive, what angular velocity should be recorded for the disk, assuming its physical motion is unchanged? a) +4 rad/s+4\,\text{rad/s} b) −2π rad/s-2\pi\,\text{rad/s} c) −4 rad/s-4\,\text{rad/s} d) 0 rad/s0\,\text{rad/s}
Intuitive explanation

The key insight is that angular velocity is a vector quantity whose sign depends entirely on your choice of axis direction—the disk's actual spinning motion hasn't changed at all. When you flip which direction counts as positive (from clockwise to counterclockwise), you're reversing the sign convention, so any velocity that was +4 rad/s+4\,\text{rad/s} in the old system becomes −4 rad/s-4\,\text{rad/s} in the new one. Think of it like changing which way you point your right thumb along the rotation axis: the same physical motion now points the opposite way relative to your new reference.

Intuitive explanation

The key insight is that angular velocity is a vector quantity whose sign depends entirely on your choice of axis direction—the disk's actual spinning motion hasn't changed at all. When you flip which direction counts as positive (from clockwise to counterclockwise), you're reversing the sign convention, so any velocity that was +4 rad/s+4\,\text{rad/s} in the old system becomes −4 rad/s-4\,\text{rad/s} in the new one. Think of it like changing which way you point your right thumb along the rotation axis: the same physical motion now points the opposite way relative to your new reference.

Browse the problem library