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).

>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.
>A hoop spinning about its center. Total mass is M and the radius is R.
>A solid disk spinning about its center. Total mass is M and a radius of R.
>A hoop spinning about its center. Total mass is 2M and a radius of R.

Explanation / Answer

Torque acting on the object to make them roation                        = I Since the torque is same then angular acceleration inversely proportional to moment of inertia. Moment of inertia of object with mass 2M                   I1 = (2M) R2 Moment of inertia of hoop of mass M                   I2 = MR2 Moment of inertia solid disk of mass M                   I3 = 1/2 MR2 Moment of inertia of hoop of mass 2M                   I4= 2MR2 Moment of inertia solid disk of mass M                   I3 = 1/2 MR2 Moment of inertia of hoop of mass 2M                   I4= 2MR2 Moment of inertia of hoop of mass 2M                   I4= 2MR2 --------------------------------------------------------------------------------------------- Rank the object in order of the resultant angular acceleration                   3 > 2 >1 = 3

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