FP8 The 32kg disk is subjected to the couple moment of M 9t

FP8

The 32-kg disk is subjected to the couple moment of M = (9t) N. m, where t is in seconds determine the angular velocity of the disk when t = t = 9 is starting from rest

Solution

>> As, Moment, M = Inertia(I) * Angular Acceleration ()

Now, here, Moment of Inertia of Disc, I= M*R²/2 = 32*0.3²/2 = 1.44 Kg-m²

and, = Angular Acceleration = dw/dt,

where, w = Angular Velocity

>> As, M = 9t

>> So, putting all in above Equation,

=> 9t = 1.44*dw/dt

=> 9t dt = 1.44 dw

Now, Integrating both sides from, t = 0, w = 0, to t = 9 sec, w = ?

=> 4.5* | t² |₀⁹ = w - 0

=> w = 364.5 rad/s ........... Required Angular Velocity .......ANSWER.......