# Cross Product problem

1. May 6, 2012

### sparkle123

Background: we're trying to show that the rate of change of angular momentum of an object about its center of mass (position given by R) is equal to the total torque about R.

Why are the terms in red equal to 0? If anything, shouldn't the terms circled in in blue be equal to zero since the vectors R and ai are parallel and ri and ai are parallel?

Thank you!

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2. May 7, 2012

### tms

What would it mean if, as you say, the acceleration of each individual particle were parallel to $\vec R$?

Last edited: May 7, 2012
3. May 7, 2012

### sparkle123

Then there is no angular momentum and only linear momentum?

EDIT: actually i made an error with my question. the new image is attached.
If ri and ai are parallel, shouldn't the cross-product be 0? So in the last line, the Ʃ miri` × A would be left instead?

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4. May 7, 2012

### tms

No. Reexamine your assumption.

Why do you think they are parallel?

5. May 7, 2012

### sparkle123

Isn't a the double derivative of r (so they are parallel)?
Thanks again!!

6. May 8, 2012

^bump

7. May 9, 2012

### tms

That doesn't mean they must be parallel. If it did, it would mean that you could change the forces on an object just by moving the origin of the coordinate system.