A wheel is rotating about an axis that is in the z-direction. The...

Question

A wheel is rotating about an axis that is in the z-direction. The angular velocity ω_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. (a) Is the angular acceleration during this time interval positive or negative?

Accepted Answer

Welcome back everybody. We are looking at a disk that is revolving with certain metrics that were given. We are told that at the time of zero seconds that it has an initial angular velocity of negative 4.8 radiance per second. Were then told that a couple of seconds later, seven seconds later, to be precise, we have a final angular velocity Of 8.9 radiance per second. And we are tasked with finding both the magnitude and the sign of our angular acceleration. I'm gonna use this kid a magic formula that says that our final angular velocity is equal to our initial angular velocity plus our angular acceleration times, time rearranging this equation a little bit and isolating Our angular acceleration yet that this is equal to our final angular velocity minus our initial angular velocity. All divided by the total amount of time that has passed. Which going from 0-7 is just seven seconds. So let's go ahead and plug in our values here we have that. Our angular acceleration is uh sorry 8. -2.8 divided by seven. Which when you plug into a calculator you get a positive 1.96 radiance per second squared which it makes sense that our angular acceleration is positive because our angular velocity is increasing over time and this corresponds to our final answer. Choice of E. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one

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