How Do You Calculate Angular Acceleration of a Disk?

[jonnyboy]

[SOLVED] Angular acceleration of disk

For the system below, determine the tension in each rope, the linear acceleration of each mass and the angular acceleration of the disk. [tex]\ g=10 m/s^2[/tex]. Use [tex]\ I=4 kgm^2[/tex].

So far I have drawn the free-body diagram for m1 and m2
[tex]\ 120 - T_1 = 12a_1[/tex] and [tex]\ T_2 - 40 = 4a_2[/tex]
and have figured [tex]\ T_1 - 2T_2 = 4\alpha[/tex]
[tex]\ a_2 = 2\alpha[/tex]
[tex]\ a_1 = \alpha[/tex]

 

[Doc Al]

So far I have drawn the free-body diagram for m1 and m2
[tex]\ 120 - T_1 = 12a_1[/tex] and [tex]\ T_2 - 40 = 4a_2[/tex]
and have figured [tex]\ T_1 - 2T_2 = 4\alpha[/tex]

So far, so good!

[tex]\ a_2 = 2\alpha[/tex]
[tex]\ a_1 = \alpha[/tex]

Excellent. Now use this to rewrite [itex]a_1[/itex] and [itex]a_2[/itex] in terms of [itex]\alpha[/itex] in your first two equations. Then you'll have three equations and three unknowns, which you can solve.

 

[jonnyboy]

Thanks. I've got it from there. Just didn't realize how easy it was once I had that.