The angular velocity of a process control motor is ω = ( 20 ─ ½ t² ) rad/s, where t is in seconds. a. At what time does the motor reverse direction?

Video transcript

Hi, everyone. In this practice problem, we will be asked to determine when will a chef experience reversal in its direction of rotation. We will have a chef acted on by multiple torques having an angular velocity given by the equation of Omega equals five minus 0.2 D squared. And D here is going to be in seconds. We're being asked to determine when will the chef experience reversal in its direction of rotation? And the options given are a 10 seconds. B five seconds c 25 seconds and D one seconds. So let's model the shaft as a rotating rigid buddy, the chef will experience a reversal in its direction at its turning point. So at the turning point or I'm gonna write down reversal will equals or will be found at the turning point. So at the turning point, our angular velocity or Omega is going to equals to zero. So when the shaft reverses its direction, Omega will be equals to the equation given which is five minus 0.2 T squared. And that will equals to zero at the reversal or at the turning point. So we want to solve this equation by equaling it to zero. So then rearranging this five will then equals to 0.2 T squared. Uh rearranging this further more T squared will then equals to five divided by 0.2. And that will give us a T squared value of taking the square root of 25. We will then be able to solve T. So T will then equals to the square root of 25 that will equals five seconds. So the chef will experience reversal in its direction of rotation at P equals five seconds, which will correspond to option B in our answer choices. So option B is going to be the answer to this particular practice problem and that'll be it for this one. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be it for this video. Thank you.