CP CALC The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt2, where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (b) What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?

Video transcript

Welcome back everybody. We are given the formula for angular velocity As a function of time for some particle on a rotating disk. And it is given as follows. C. Which is a constant equal to 3.25 plus d. Another constant which .5 times I'm squared. And we are asked to find what the angular acceleration is at times zero and what the angular acceleration is at times 3.6. Well first to figure out these we need angular acceleration As a function of time so that we can plug in T values. This is just gonna be equal to the derivative of our angular velocity with respect to time. So let's go and take the derivative of this function right here from my term river 3.25 It's gonna be zero because that's a constant plus the derivative of this term. So using the power rule we're gonna have this to come down in front times 0.85 times our time. This is equal to 1.7 radiance per second cubed times. I'm Now that we have that. Let's go ahead and plug in our values. So acceleration evaluated at zero is equal to 1.7 times zero which is just zero radiance per second squared. Now our angular acceleration at time 3.6 seconds is equal to 1.7 times 3.6. Which when you plug into your calculator you get 6.12 radiance per second squared. So we have now found our two angular accelerations or responding to answer choice c. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.