Given w = T (v), where T is a linear transformation and w and v are vectors, why is it that we can write any coefficient of w, such as w1 as a linear combination of the coefficients of v? i.e. w1 = av1 + bv2 + cv3
Supposably this is a consequence of the definition of linear transformations, but...
I've attached the problem and solution as picture. To my understanding, the gear E and the rod OB are taken together as the rotating rigid body. However, the equations of motion and (##∑F = macm##)
are applied to the center of mass of the rod, G, rather than the center of mass of the rigid body...
Ok I see. The field is zero at the center of a spherical charge distribution, no matter the size of sphere. So if our charge had dimensions (unlike a point charge), then the field would be zero at the origin.
I checked some books and you are right. However, I don't understand why we can't we just assign it a value of zero? After all, the charge cannot apply force on itself.
The derivations of formulas in textbooks on thermodynamics and fluid mechanics seem to repeatedly make the assumption that the volume of whatever chosen control volume is constant, that's why I had to ask.
Control volumes are used to analyze transient and continuous processes alike; Refer to an engineering thermodynamics textbook. The point is that it's a mathematical tool that provides a different point of view from the lagrangian/control mass viewpoint. A transient process can lend itself to...