Why Do Torques Use a Negative Sign in Inverted Pendulum Equations?

[Arslan]

i have problem with the equation encircled in red in the figure. I(theeta)''=sum of all torqes acting on the body. but they are taking torques in the negative direction why.
It should be -VLsin+HLcos=I(theeta)''

 

[Doc Al]

i have problem with the equation encircled in red in the figure. I(theeta)''=sum of all torqes acting on the body. but they are taking torques in the negative direction why.
It should be -VLsin+HLcos=I(theeta)''

Because the way theta is defined (with respect to the vertical) it increases in the 'negative' (clockwise) direction. If they defined theta with respect to the horizontal then you'd be correct.

 

[Arslan]

but the body is rotating along its center of gravity. If the force is applied on cart, the cart will move in the forward direction and transfer the force to the rod in the direction of red arrow, and the body will rotate along its center of gravity. So body is rotating in counter clockwise direction.

 

[Doc Al]

but the body is rotating along its center of gravity. If the force is applied on cart, the cart will move in the forward direction and transfer the force to the rod in the direction of red arrow, and the body will rotate along its center of gravity. So body is rotating in counter clockwise direction.

All true, but irrelevant. It's just a matter of sign convention. Since theta is defined in the clockwise direction, torques in the clockwise direction will be positive.