A phasor of length 4 begins at 0° . If it is rotating at ω = 250 s −1 , what is the value of the phasor after 0.007 s?

Hey guys. I hope you're able to solve this problem on your own. If not, here's a little bit of help. A phaser of length 4 begins at 0 degrees. If it's rotating at omega equals 250 inverse seconds, what is the value of the phaser after point 007 seconds, okay? So, we are assuming that this phaser starts at 0 degrees because that's what the problem says. Okay. Now this phaser doesn't have a physical meaning associated with with it. We're not told if it's current or voltage or whatever, but that doesn't actually matter. It's just some arbitrary phaser with a length of 4. Okay? Now, how far does it rotate after 0.007 seconds is gonna be important to draw on this phaser in its final position. Recall that theta, that distance which is omega t is going to be 250, right, omega times the amount of time, 0.007 seconds, and that is going to be 1.75 radians, which converting it gives us a 100 degrees. Okay? So a 100 degrees is going to be in the second quadrant because it's greater than 90. So this rotates past the vertical y axis, sorry, the positive y axis, the vertical axis, and it is now here with the length of 4. This is 100 degrees. We could also say that this this angle right here was 10 degrees if we wanted to. Okay? Now, we wanna find its value. Remember that a phaser's value is always how far it extends on the horizontal axis. Okay? It's going to be this projection right here. That's going to be the phasor's value, or the value is just going to be the magnitude times cosine of its angle. Okay. You can do cosine of a 100 degrees if you want. That's gonna give the value as a negative value, which it should be because it's pointing to the left. It's on the negative horizontal axis, axis so it should absolutely be negative. If you wanted to, you could also say that this angle right here was 80 degrees, right? Because this angle is 10 and you could use cosine of 80 degrees. That would give it as a positive value and you would have to remember to make sure to add a negative sign but either way, you'll get the correct answer. Plugging this in, we get negative 0.713. Okay? So, whatever this was, if it was a current, if it was a voltage, it switched signs from positive to negative and its magnitude was 4 and its current value, its instantaneous value, is negative 0.713. Alright guys. Thanks for watching.

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Multiple Choice

A phasor of length 4 begins at 0° . If it is rotating at ω = 250 s⁻¹ , what is the value of the phasor after 0.007 s?

0.2

0.7

3.1

3.9

4.0

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A phasor of length 4 begins at 0° . If it is rotating at ω = 250 s−1 , what is the value of the phasor after 0.007 s?

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A phasor of length 4 begins at 0° . If it is rotating at ω = 250 s⁻¹ , what is the value of the phasor after 0.007 s?