# Does weight distribution affect angular velocity?

If an equal torque of equal radius and size is produced on two bodies of the same weight and same center of gravity, but with different weight distribution (say one has a 1kg mass 1 meter above the center of mass, while the other has it 10 cm above). Will this affect the angular velocity of it?

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Is the axis of rotation vertical? – Qmechanic Jan 16 '13 at 19:15

## 1 Answer

Yes, it will affect angular velocity since different mass distribution have different moment of inertia $I$ in general. The effect of torque $\tau$ on the angular velocity $\omega$ of the object is given by $$\tau=\frac{d}{dt}(I\omega)$$

The moment of inertia of a point mass is given by $I=mr^2$, so in your case, the radius differ by 10 time so moment of inertia differ by 100 times and so does the angular velocity. Note that when you mention torque, you dont necessary need to specify which point it acts on.

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"you dont necessary need to specify which point it acts on" but you do need to specify in some way the plane of induced rotation. If you use the (pseudo-)vector given by the cross-product you get that for free. – dmckee Jan 16 '13 at 19:47
@dmckee Ya, we still need to specify that as it is a vector quantity. I forget to mention that. – hwlau Jan 16 '13 at 19:50