Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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?

share|improve this question
    
Is the axis of rotation vertical? –  Qmechanic Jan 16 '13 at 19:15
add comment

1 Answer

up vote 1 down vote accepted

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.

share|improve this answer
    
"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
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.