#Angle of friction:The angle between resultant value of normal reaction and friction force to the normal reaction is called angle of friction. It is denoted by alpha.

# Angle of repose: The angle made by the inclined surface with the horizontal for which the body kept over the inclined surface just begins to slide is called angle of repose.

For angle of friction 

       Consider ‘m’ be mass of body, ‘Fs’ be friction force, ‘ma’ be force applied and ‘R’ be normal reaction.
From figure and definition of angle of friction           

     Tanα=PQ/OP
or, Tanα=ON/OP
or, Tanα=Fs/R ......................(i)

Again,
         Coefficient of friction (ɰ)=Fs/R..............................(ii)
      From equation(i) and (ii)
          Tanα=ɰ..................................(A)
Hence,the coefficient of limiting friction is equal to the tangent of angle of friction.
 
 
For angle of repose
       
     Consider ‘m’be mass of object with weight mg.mg resolved into two component mg cosፀ and mg sinፀ.mg cosፀ balance the normal reaction ‘R’ and mg sinፀ balance the friction force ‘Fs’ where ፀ is the angle of repose.
We know,
  Normal reaction (R)=mg cosፀ.............(1)
  Frictional force (Fs)=mg sinፀ...............(2).                  

 Dividing equation (2 )by (1)
     Fs/R=mg sinፀ/mg cosፀ
or,Fs/R=Tanፀ
Also, Fs/R=ɰ [ ɰ is cofficient of friction ]
 or,Tanፀ=ɰ............................(B)
From equation (A) and(B)
     Tanα= Tanፀ
Therefore, α=ፀ
Hence, angle of friction is equal to angle of repose



















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