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CBSE Class 11-science Answered

Derive an expression for torque in polar co-ordinate.
Asked by Topperlearning User | 12 Aug, 2014, 03:12: PM
answered-by-expert Expert Answer

Let the line of action of force  makes an angle α with x-axis.

     

                             Figure d    

           

 

The two rectangular components of Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '. are :

 F x= F cos α  &  F y= F sin α)----------------------------(1) 

If x,y are the coordinates of the point P,then 

x= r cos θ & y = r sinθ--------------------------------(2)

where Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '.

Substituting the values of Fx, Fy, x & y in the equation =(x F y - y F x )

                   =(x F y - y F x )

                             = (r cos θ) F sin α - (r sinθ) F cos α

                     = r F [sinα cosθ - cos α sin θ]

                     = r F sin(α - θ)------------------------------------------ (3)

Let Φ be the angle which the line of action of  makes with the position vector Syntax error from line 1 column 49 to line 1 column 73. Unexpected '<mstyle '..

As clear from the figure

                       θ + Φ= α

                  or  Φ = α - θ

On substituting this values in eq (3), we get

                            = r F sin Φ

This is the expression for torque in polar co-ordinate.

Answered by | 12 Aug, 2014, 05:12: PM
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