Question

The 165-lb flywheel has a radius of gyration about its shaft axis of k=20in. and is subjected to the torque M=8(1−e −t )lb−ft, where t is in seconds. If the flywheel is at rest at time t=0, determine its angular velocity ω at t=3 sec.

Answer 1

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.

Step-by-step 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.