Answer
The new angular acceleration will be 32 times smaller than the old one.
Work Step by Step
With each of the 3 dimensions being twice as great, the volume of the new object will be (2)(2)(2) = 8 times as great as the old object, and so will the mass.
Using equation 9.16 to calculate the moment of inertia, we see that each distance $r_i$ is twice as great as before, so that increases the moment of inertia by another factor of $2^2 = 4$.
Overall, the object’s moment of inertia is 32 times what it was before.
The same torque is applied to both objects.
$$\Sigma \tau = I\alpha$$
$$\alpha = \frac{\Sigma \tau }{I}$$
With a new moment of inertia I that is 32 times larger, the new angular acceleration will be smaller by a factor of 32.
