How Can Vector Analysis Improve Understanding of Mechanics Problems?

[Tanya Sharma]

The solution is very simple if you choose the coordinate system so that point A is at (X,0) and point B is at (0,Y). Then the CM is at (X/2, Y/2) and

V_CM= 0.5 (dX/dt, dY/dt)

As the length of the rod is constant, X² + Y²=0, so

X dX/dt+Y dY/dt=0,

dX/dt=V, dY/dt=-(X/Y) V.

X/Y can be written with the angle of inclination, so you get dY/dt in terms of V and the angle.

ehild

I am pretty embarrassed by seeing such an elegantly simple solution

The problem is that I don't think in terms of vectors .Rather I was treating velocities as if they were scalar quantities .

Thanks ehild !

 

[jhae2.718]

The problem is that I don't think in terms of vectors .Rather I was treating velocities as if they were scalar quantities .

As some general advice to you and any other interested reader, you will find that kinematics are far easier (and arguably more intuitive) when you work with vectors. Vector analysis is an extremely powerful tool and is the foundation of much of mechanics.

 

[Tanya Sharma]

As some general advice to you and any other interested reader, you will find that kinematics are far easier (and arguably more intuitive) when you work with vectors. Vector analysis is an extremely powerful tool and is the foundation of much of mechanics.

Thank you very much for the advice.I really appreciate it.

Could you suggest me some book or reference material which specifically use vector analysis to tackle mechanics problems .The general introductory physics books hardly use vectors .

 

[coldblood]

Use v = -ωLsinθ .

Substitute value of ω in the expression for α .

Thank you Tanya I got the answer.

 

[jhae2.718]

Could you suggest me some book or reference material which specifically use vector analysis to tackle mechanics problems.

In my opinion there's a bit of a gap in mechanics textbooks between the simplistic treatments in introductory physics and sophomore-level dynamics and advanced treatments of analytical mechanics.

Depending on your level of mathematics (you should have at least basic and vector calculus; linear algebra is helpful, as is differential equations), I think Anil Rao's book Dynamics of Particles and Rigid Bodies: A Systematic Approach isn't that bad of an option; I find myself in agreement with much of the principles Rao enumerates in the forward to his text on the necessity for teaching rigorous vector mechanics. I'm a little hesitant in this recommendation, as I think this may be too large a jump from basic introductory physics, but with some effort I think it should be manageable.

Also, keep in mind that I am an aerospace engineer and thus my approach to the subject is biased in that direction; some of the physicists here may chip in with other opinions.