The discussion revolves around the use of negative signs in the torque equations for an inverted pendulum, particularly focusing on the definition of the angle theta and its implications on torque direction. Participants explore the relationship between the direction of rotation, the application of forces, and the resulting torque calculations.
Participants express differing views on the direction of rotation and its impact on torque signs, indicating that multiple competing perspectives remain unresolved in the discussion.
The discussion highlights the dependence on the definition of angle theta and the implications of sign conventions in torque calculations, which may not be universally agreed upon.
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 said: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)''
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.Arslan said: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.