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. $$\ g=10 m/s^2$$. Use $$\ I=4 kgm^2$$.

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

 

[Doc Al]

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

So far, so good!

$$\ a_2 = 2\alpha$$
$$\ a_1 = \alpha$$

Excellent. Now use this to rewrite $a_1$ and $a_2$ in terms of $\alpha$ 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.