CBSE Class 11-science Answered
Let the line of action of force makes an angle α with x-axis.
Figure d
The two rectangular components of 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
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 .
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.