1. Write the equations of motion which govern the motion of centre of mass 

2. Derive an expression for torque in cartesian coordinates

Asked by fishtailfever | 3rd Nov, 2019, 11:01: PM

Expert Answer:

begin mathsize 14px style a subscript C M end subscript space equals fraction numerator begin display style sum from i equals 1 to n of end style m subscript i a subscript i over denominator begin display style sum from i equals 1 to n of end style m subscript i end fraction end style
where aCM is acceleration of centre of mass, ai is acceleration of individual objects that hass mass mi
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Torque τ of force F acting on a body is,  τ = r × F
 
where r is position vector of point of application of force with respect to reference point.
 
Let begin mathsize 14px style r with rightwards arrow on top space equals space x space i with hat on top plus space y space j with hat on top space plus space z k with hat on top space end style and begin mathsize 14px style F with rightwards arrow on top space equals space F subscript x space i with hat on top plus space space F subscript y space j with hat on top plus space space F subscript z k with hat on top end style.
Then the torque τ is given by
 
begin mathsize 14px style tau with rightwards arrow on top equals space open vertical bar table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row x y z row cell F subscript x end cell cell F subscript y end cell cell F subscript z end cell end table close vertical bar space equals space left parenthesis space y space F subscript z minus z space F subscript y right parenthesis space i with hat on top space minus left parenthesis space x space F subscript z minus z space F subscript x right parenthesis space j with hat on top space plus left parenthesis space x space F subscript y minus y space F subscript x right parenthesis space k with hat on top space end style

Answered by Thiyagarajan K | 4th Nov, 2019, 08:04: AM

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