What is the Vector r in the Ferris Wheel Momentum Problem?

[fball558]

Ferris wheel question!

Homework Statement

A common amusement park ride is a Ferris wheel (not drawn to scale). Riders sit in chairs that are on pivots so they remain level as the wheel turns at a constant rate. Assume the usual coordinate system (x to the right, y up, z out of the page, toward you.)

A particular Ferris wheel has a radius of 22 meters, and it makes one complete revolution around its axle in 20 seconds. In all of the following questions, consider this location (at the center of the axle) as the location around which we will calculate the angular momentum. At the instant shown in the diagram, a child of mass 38 kg, sitting at location F, is traveling with velocity < -6.9, 0, 0> m/s.
(location F is at the very bottom of the Ferris wheel "lowest point" I could not get the pic to get on here)

What is the momentum of the child?
= < -262.2, 0, 0 > kg·m/s ##I already found this already and it is right the next part is where my question is.

In the definition L = r x p what is the vector r ?
r = <??, ??, 0 > m need to find x and y the r here has an arrow above it
What is r perpendiculat?
r = 22 m i found this as well really just ned the x and y of r (has arrow above it)

The Attempt at a Solution

i found p from above. used La = r x p
La i said was m x r perpendicular so 38 x 22 got 836
then did 836 = r x -262.2
then got r = -3.188
but that does not sound right
any help would be great.

 

[Dr.D]

In terms of the unit verctors i,j,k, the vector r = -22 j because it is below the origin of coordinates. Use that in your cross product and ssee how it turns out.

 

[jchojnac]

I still don't understand how you get the vector r.

 

[LowlyPion]

I still don't understand how you get the vector r.

For finding angular momentum r is the displacement vector from the point of interest. For your situation you have

L = r X p = <0,-22 j, 0> X <262 i, 0,0>

If you draw a picture, the girl is at the bottom moving horizontally <i>. And the r vector is pointing down <-j>

 

[fball558]

i got it by just finding the x and y component compared to the axis.
for example, my person was at the very bottom directly below the axel
so my x component was 0. my y component was was just the negative radius. if your position is a diagonal just set up a right triangle to find the x and y components
works for me can try it for yours and see if you get it then.