- #1
Cedric Chia
- 22
- 2
I' m trying to derive the work done by a torque from W = ∫ F ⋅ ds and I' ve looked up the internet, it said:
W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 )
it can be written as
W = ∫ F ⋅ dθ x r
this is a vector triple product , thus can also be written as
W = ∫ r × F ⋅ dθ
W = ∫ Torque ⋅ dθ ----------------------------------------------------- ( Line 2 )
My question is :
In what direction is dθ pointing so that when I cross-product dθ and r ( Line 1 ), it become ds ? And also, when I dot-product Torque and dθ ( Line 2 ) , what is the angle between them ?
W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 )
it can be written as
W = ∫ F ⋅ dθ x r
this is a vector triple product , thus can also be written as
W = ∫ r × F ⋅ dθ
W = ∫ Torque ⋅ dθ ----------------------------------------------------- ( Line 2 )
My question is :
In what direction is dθ pointing so that when I cross-product dθ and r ( Line 1 ), it become ds ? And also, when I dot-product Torque and dθ ( Line 2 ) , what is the angle between them ?