A flywheel with a moment of inertia of 5.0 kg-m ^2 is rotated at a speed of 60 rad/s . Due to friction at the axle, it comes to rest in 5.0 minutes . Determine the angular momentum of the wheel 1 minute before it stops rotating.

Step-by-step solution

Initial angular velocity, ₀ = 60 rad/s Time taken to come to rest, t = 5.0 minutes = 300 s Final angular velocity, = 0 Using the first equation of rotational motion, = ₀ + t 0 = 60 + (300) = - 60 300 = -0.2 rad/s ^2 We need to find the angular momentum 1 minute ( 60 s ) before it stops. The time elapsed from the start is t' = 5.0 - 1.0 = 4.0 minutes = 240 s . Angular velocity at t' = 240 s is given by: ' = ₀ + t' ' = 60 + (-0.2)(240) = 60 - 48 = 12 rad/s Angular momentum at this instant is: L = I ' L = 5.0 12 = 60