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How does torque arises when not bending forward and how does it gets cancelled while bending little forward? Please give me a video explanation or figurative explaination if possible.

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  • $\begingroup$ you can rise from the chair being straight too(it depends on ow youuse your muscles) $\endgroup$
    – Anonymous
    Commented Dec 5, 2020 at 6:44

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The force of gravity can be thought of as acting on you through what is called the "center of gravity." Your center of gravity will be at the same position as your center of mass. The force of gravity acts through the center of mass.

Consider the sketch below:

enter image description here

The blue point is the center of mass, and the red point $P$ is your pivot (point about which you rotate). Green vector is the radius vector $\vec r$. Blue vector is the force of gravity.

Case A. When you are sitting on a chair, your back is to the right of the pivot, and so your center of mass will be clearly to the right of the pivot. Gravity will act through the COM, and there is a clockwise torque exerted on you by gravity.

Case B. When you lean forward, you shift your center of gravity forward. Remember that gravity acts through the center of gravity. Then, notice that the angle between the $\vec r$ and $\vec F$ vectors gets closer to $180^\circ$ (i.e. $\sin\theta$ goes to $0$ as $\theta \to 180^\circ$)**, because your center of gravity will be almost right above the pivot point. Recall the formula for torque magnitude due to gravity: $$\tau = mgr\sin\theta$$

Notice that when your center of mass is (more or less) right above the pivot, the angle between $\vec r$ and $\vec F$ approaches $180^\circ$, thus $\sin\theta$ gets smaller and approaches $0$. Therefore, the clockwise torque exerted onto you by gravity (which prevents you from rising) decreases.

Case C. You lean even more forward. At this point, the torque by gravity will be counterclockwise. This counterclockwise torque will help you get up (because it is making you rotate in the direction you are already trying to go).

Alternatively, you could position yourself such that your center of gravity is right above the pivot, in which case there is no net torque, and you could rise up vertically by pushing your feet against the ground. However, in practice, positioning yourself like that is difficult, so there will be some net torque.

Therefore, by leaning forward, you are shifting your center of gravity forward such that the torque due to gravity will rotate you forward in the counterclockwise (which is the direction you want to go), because the torque is now counterclockwise.

So, what leaning forward does, is provides you with the necessary counterclockwise torque allowing you to get up. Though note that counterclockwise torque could have also been provided by pushing the chair with your hands, but for our purposes, let's keep things simple and assume you don't.

Thank you user @Umaxo to for the edit suggestion.

**Also, recall that when measuring angles between vectors, you measure the angle when the vectors are tail to tail.

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  • $\begingroup$ thank u so much. It was way better than i expected. $\endgroup$ Commented Dec 5, 2020 at 15:45
  • $\begingroup$ @CREATIVITY Unleashed thank you, glad it helped. If this post fully answers your question, [lease consider accepting the answer :) $\endgroup$
    – user256872
    Commented Dec 5, 2020 at 20:57
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When you are sitting in a chair, any movement left or right will generate a torque which will cause the chair to spin. But if you tilt your body forward, you move your centre of mass away from the chair’s axis of rotation. Because of conservation of angular momentum, this will cause the chair to stop spinning rather quickly.

The same principle as the figure skater who extends their arms to slow down applies here.

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Try sitting straight and push the arms of your chair to get up. You will notice that you don't always need to bend forward to rise from the chair instead a reaction force is exerted on you by the chair which helps you to get up. Similarly, in case you are trying to get up without using your hands you bend your body to generate a force which will try to push the floor backwards which in turn produces a reaction force which helps you to get up. All you need is a reaction force which will give you a lift.

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