A series of object are being rotated. The same net torque is being applied to ea

Question

A series of object are being rotated. The same net torque is being applied to each object. Rank the object in order of the resultant angular acceleration (1=lowest).
1. A solid sphere spinning about its center. Total mass is 0.5M and the radius is R.
2. An object consisting of two objects connected by a massless rod. Each object has a mass of 2M and is a distance R from the axis of rotation.
3. A solid disk spinning about its center. Total mass is 0.5M and the radius is 2R.
4. A solid disk spinning about its center. Total mass is M and a radius of R.

Explanation / Answer

Torque = Ia, so its all based on the value of I, the moment of Inertia. The larger moment of Inertia, the smaller the angular acceleration, so...

The disk has an I of .5MR^2

The sphere has an I of 2/5 MR^2

The objects on the rod are 4MR^2

The last solid disk where M = .5M and R = 2R, so I = .5(.5M)(4R^2) = MR^2

So, all of the MR^2 can be ignored, and thus you see that...

The objects on the rod have a value of 4

The last sold disk has a value of 1

The first solid disk has a value of .5

The solid sphere has a value of .4

So, in order of smallest to largest...

1 = The objects on the rod

2 = The last sold disk

3 = The first solid disk

4 = The solid sphere

In order of the way you have them listed, that is 3, 4, 1, 2

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