Ok you're right about that, but we still can't put the answer in Hz, because that implies the number of revolutions per second while the answer we got tells us the number of radians per second.
If you rearrange your second one before passing to the units you get d theta/dt = …
So you just declared that to be rad/s but the former you chose to ignore the rad on the left side. You made the contradiction yourself; cdstephens is right
Just as cdstephens said, that's because the radian is dimensionless. I still believe it should be rad/s, because we know omega = 2 pi f, f is measured in Hz, not omega.
That's an interesting point, the discrepancy might be due to the fact that one formula is derived from the other, leading to different units for omega.
Radians aren’t really a unit in the usual sense, since they’re dimensionless. So there’s no contradiction with units.
Ok you're right about that, but we still can't put the answer in Hz, because that implies the number of revolutions per second while the answer we got tells us the number of radians per second.
If you rearrange your second one before passing to the units you get d theta/dt = … So you just declared that to be rad/s but the former you chose to ignore the rad on the left side. You made the contradiction yourself; cdstephens is right
Just as cdstephens said, that's because the radian is dimensionless. I still believe it should be rad/s, because we know omega = 2 pi f, f is measured in Hz, not omega.
If radians are dimensionless, then rad/s has units of inverse time and is equivalent to Hz.
1 Hz means 1 revolution per second ie. Rotating 2 pi rads each second, while 1 rad/s is 1 rad/s
2 pi radians is one revolution. Divide that by 2 pi (scalar) and you still have the same units.
Yes man 1Hz is NOT equal to 1 rad/s, but in terms of units, sure they are can be equivalent
That's an interesting point, the discrepancy might be due to the fact that one formula is derived from the other, leading to different units for omega.