The figure below shows three disks (of the same radius) that can rotate about th

Question

The figure below shows three disks (of the same radius) that can rotate about their centers like merry-go-rounds. Each disk is made of the same two materials, one denser that the other. In disks 1 and 3, the denser material forms the outer part of the disk area. In disk 2, it forms the inner part of the disk area. Forces with identical magnitudes and directions are applied tangentially to each disk, either at the outer edge or at the interface of the two materials, as shown. (a) Rank the disks according to the torque acting on the disk about its center. (b) Rank the disks according to the rotational inertia (moment of inertia) of the disk about its center.

Explanation / Answer

a)

Since,

T=r X F

and r and F are same for 1 and 2 and less for the disc 3,

1=2>3

b)Because the denser material is far on bothe the disks and

I=mr^2

1=3>2

c)

Since, T=Ialpha

where alpha is angular accelaration,

And T= Torque is same for 1 and 2 the bodies but mment of inetia of 1>2,

Angular accelaration is inversely proportional to I,

Hence,

3>1<2

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