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Answer :
Final answer:
To determine the angular velocity of the flywheel at t = 3 seconds, calculate the angular acceleration and integrate it to find the change in angular velocity.
Explanation:
To determine the angular velocity of the flywheel at t = 3 seconds, we need to find the angular acceleration first. The torque, M, can be written as M = Iα, where I is the moment of inertia and α is the angular acceleration. From the given torque equation, M = 8(1−e^-t) lb-ft, we can solve for α by rearranging the equation as α=(1/I)dM/dt.
To find ω at t = 3 seconds, we can integrate α with respect to t from 0 to 3 seconds to find the change in angular velocity. ω = ∫(0 to 3)αdt.
Finally, substitute the values into the equation to calculate the angular velocity ω at t = 3 seconds.
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