Cross Product in Uniform Circular Motion

[snoggerT]

Homework Statement

A centripetal-acceleration addict rides in uniform circular motion with period T = 3.22 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2) i + (-9.00 m/s2) j. At that instant, what are the following values?

(b) r X a

The Attempt at a Solution

I'm really stumped on this one. I completely understand how to do cross products of a vector, but there is nothing in my textbook about doing a cross product problem in uniform circular motion. I tried taking the magnitude of a and multiplying it to times r, but that wasn't right. If anyone can give me a hint as to how to start this, I would be very thankful.

 

[nrqed]

Homework Statement

A centripetal-acceleration addict rides in uniform circular motion with period T = 3.22 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2) i + (-9.00 m/s2) j. At that instant, what are the following values?

(b) r X a

The Attempt at a Solution

I'm really stumped on this one. I completely understand how to do cross products of a vector, but there is nothing in my textbook about doing a cross product problem in uniform circular motion. I tried taking the magnitude of a and multiplying it to times r, but that wasn't right. If anyone can give me a hint as to how to start this, I would be very thankful.

what do you know about the acceleration vector in uniform circular motion?

 

[snoggerT]

what do you know about the acceleration vector in uniform circular motion?

- I know that acceleration is always concentrated toward the center and is always perpendicular to the objects velocity. I know that a=v^2/r . I think that's about it...

 

[nrqed]

- I know that acceleration is always concentrated toward the center and is always perpendicular to the objects velocity. I know that a=v^2/r . I think that's about it...

Right. So in the formula $\vec{r} \times \vec{a}$, assuming that by the vector "r" they mean the vector pointing from the center of the circle to the position of the object, you know that these two vectors point in opposite directions. What can you say about the cross product of two vectors pointing in opposite directions?

 

[snoggerT]

Right. So in the formula $\vec{r} \times \vec{a}$, assuming that by the vector "r" they mean the vector pointing from the center of the circle to the position of the object, you know that these two vectors point in opposite directions. What can you say about the cross product of two vectors pointing in opposite directions?

that their product would be 0. Thanks for the help. I just wish the textbook explained things worth a crap.

 

[nrqed]

that their product would be 0. Thanks for the help. I just wish the textbook explained things worth a crap.

You're welcome. When you have questions about the cross product, there are two ways to go: through components or through the formula "magnitude of a times magnitude of b times sin (theta)".
Then think about all the information that you know about either the magnitudes of the vectors or their direction.


best luck!