Dynamics - 2 shafts rotating & connected with a clutch

[Renni202]

Dynamics -- 2 shafts rotating & connected with a clutch

During the operation of a machine, two shafts rotate in opposite directions and are then connected by a clutch system. Shaft 1 has a rotational speed of 800 rev/min, a mass of 35 kg and a radius of gyration of 375 mm. Shaft 2 has a rotational speed of 1100 rev/min, a mass of 45 kg and a radius of gyration of 520 mm. Determine:

i) the moment of inertia for each shaft;ii) the final speed and direction of rotation for the connected shafts;

iii) the angular torque developed by the connected shafts if the rotational speed increases to 900 rev/min in a time of 3.2 s.

iv) the kinetic energy of the connected shafts at the increased speed.Question: (my last question before submitting my work I promise)

I managed to work out (i) and (ii) no problem for part (iii) do I use T=Ia and then Impang= Tt? and for (iv) do I use Ekang=1/2 Iω² with the revs set at 900 rev/min?

 

[CWatters]

I managed to work out (i) and (ii) no problem for part (iii) do I use T=Ia and then Impang= Tt?

Just use T=Ia
where "I" is the combined moment of inertia
and "a" is the angular acceleration.

You have the initial and final angular velocity and the time so you can calculate the acceleration.

and for (iv) do I use Ekang=1/2 Iω2 with the revs set at 900 rev/min?

Yes.

Aside: Make sure to use the right units for the angular velocity and acceleration.