Inertia and Angular Acceleration

[CollegeStudent]

Homework Statement

Two concentric disks are welded together with a small hole through the center. This two disk unit is mounted onto a frictionless horizontal axle through the center hole. Two strings are attached and wound in opposite directions around the outer perimeter of each disk and are left hanging. The smaller disk has a mass of 4.77 kg and a diameter of 32.4 cm. The larger disk has a mass of 6.85 kg and a diameter of 44.2 cm. (a) If a mass of 400 g is hung from the string wrapped around the smaller disk, what mass should be hung from the string around the larger disk so that the two disk unit does not rotate? (b) If no mass is hung from the string around the larger disk, what will be the magnitude and direction of the acceleration of the two disk unit?

Homework Equations

The Attempt at a Solution

Not really sure what to do here...I can calculate the Inertia of the Smaller disk and the larger disk...But I don't know what to do.

I_disk = 1/2mR²

any hints here? Thanks in advance

 

[Yosty22]

The only thing I can think of is balancing the torques. If it doesn't rotate, it won't have any torque, so use the proper definition of torque to find when, with both masses and both moments, that the total torque on the system is 0.

 

[mfb]

For (a): Which property of the masses would "try" to rotate the disks? How can you get zero acceleration with those two masses?

In (b), just do the same consideration as in (a), but with a single mass and the total inertia of the system.

Edit: Yosty22 was quicker.

 

[tiny-tim]

Hi CollegeStudent!

(a) If a mass of 400 g is hung from the string wrapped around the smaller disk, what mass should be hung from the string around the larger disk so that the two disk unit does not rotate? (b) If no mass is hung from the string around the larger disk, what will be the magnitude and direction of the acceleration of the two disk unit?

For (a) you don't need moment of inertia at all, since nothing is moving …

just add the torques​

For (b), use τ_net = Iα