Question

How do I know when to use M=u*(r X F) or M= r X F to find the Momentum

Answer 1

Is that u times (r cross F) or is X a variable?\[M = u \cdot (r \times F) ~~ {\rm or}~~ M = u \cdot (r \cdot X \cdot F)\]

Answer 2

times

Answer 3

r cross F

Answer 4

u dot product ( r cross product F)

Answer 5

Okay. Another question: What quantity is u?

I want to make sure we are on the same page here. I have a feeling we are defining angular momentum here and not translation momentum.

Answer 6

u needs to be found

Answer 7

I know how to do it because the book shows it using the cartesian values but my question is when a problem is given to find M , how do I know if I use M=u*(r X F) or just M = r X F

Answer 8

I got it. You are looking to calculate the moment not momentum.

I would always use\[M = r \times F\]I don't know what u represents. If I know what it is, I can advise you on how to use it.

Answer 9

In the example you have given, to find the moment about point A, using the following expression. \[M_A = [0.6 \hat i + 0.3 \hat k] \times [-300 \hat k] = (0.6 \cdot -300) \cdot [\hat i \times \hat k] + (0.3 \cdot -300) \cdot [\hat k \times \hat k] = (0.6 \cdot 300) \hat j\]

Answer 10

\[M_A = (0.6 \cdot 300) \hat j\]

Answer 11

u is the vector AB

Answer 12

beccause the problem says find the Mab produced by the Force

Answer 13

To find the moment about point B, \[M_B = [0.2 \hat i - 0.2 \hat j + 0.3 \hat k] \times -300 \hat k\]

Answer 14

For a moment about the line through A and B, \[M_{AB} = \vec u_{A/B} \cdot (\vec r_o \times F_C)\]where \(\vec r_o\) is the vector from any point of the segment AB to C.

Answer 15

We use the vector \(\vec u_{A/B}\) when we are finding the moment about a line or axis. We use the regular cross product when we are finding the moment about a point.

Answer 16

\[M_{line} = \vec u \cdot (r_o \times F)\]\[M_{point} = r \times F\]

Answer 17

Perfect!!!!! Thank you soooooo much!!! Couldn't be explained better!!!!