Returning to our consideration of the moment of a force, and referring to Fig. 1 (same as Fig. 1 of Section: The Definition of a Moment), we now see that we can write the moment vector as:
By the definition of the vector product, this statement is equivalent to the definition of a moment given previously. The vector
The components of the vector
These are, of course, the same expressions obtained from Fig. 1. The introduction of the vector product makes possible a concise notation for moment vectors. Note that the sign convention for moments previously mentioned is consistent with the sign convention for vector products.
1.10.1 PROBLEMS
1. Show that two vectors
2. Show that both the scalar product and the vector product obey the distributive law of ordinary multiplication, i.e.,
3. Given two vectors
Find the following vectors:
answer
4. Show that the vector product can be written as
5. Given two vectors
answer
38° 11’
6. Find the moment about the point
answer
7. A body is rotating about an axis with an angular speed of
8. A body is rotating with an angular speed of 2 radians per second about an axis parallel to
