# A problem about moment (torque ) [closed]

Everybody knows that moment of a force increases with distance. However, there is a problem about it that makes me confused these days: Let's take a look at this picture

due to the formula M = F.d, the level will be balanced. And because the two object have no acceleration, there must be forces that counteract with their weights. so let's assume g=10m/s^2 and analyze the picture above.

So in this picture we can see that if we apply a force of 10N on 1 end of an arm, a 20N force will appear at a half length of the other arm with opposite direction. Now let's remove a 2kg object, and the force of 10N will cause the level to rotate an angle ( let's assume it rotates 90° ) in a specific time. When an arm rotate, the other will do the same thing in the same amount of time, however, the arc that a 1kg object move ( assume its attached to the level and will not fall off ) is bigger than the arc that a point at where the 20N force apply on travel. To be more easy to imagine, let's look at this picture.

Imagine we stick 2 apple on a level that balanced each other by their weights. Now we push the right apple with a force F upward, it will rotate, and the other will do the same, but with a bigger arc though they start and stop at the same time due to the equation v = r.w ( i can't type the omega symbol ) However, as I mentioned above, if we apply a force of 20N on the right apple, the left apple only feel 10N downward. With less force being applied, how can it move faster than the right apple?

this is my first article, if it has any mistake or hard to understand, please forgive ><.

• Please clarify if in text below the second image, you mean to say that if the block on the right was suddenly removed, the bar would rotate (clock-wise) to an equilibrium at $-90 \deg$. In that case, is the question that why the first block moves through a larger distance than the mass the point of attachment of the second mass prior to it's being removed? Mar 1, 2020 at 9:54
• @kb314 Sorry because it's hard to understand. It's clearer in the third and fourth picture, yes the question is why the 1kg block move larger arc than the point of attachment of the second block ( which is removed ), though it is applied a weaker force than the other. Mar 1, 2020 at 10:56
• What do you mean by “a 20N force will appear”? Mar 1, 2020 at 12:22
• @Bob D If I put a 1kg on one end of an arm and 2kg at a half the length of the other arm, they will balance each other. Because both objects are balanced which means they don't move => zero acceleration => there must be forces counteract with their weights, so their will be a 20N upward force apply on the 2kg object when the 1kg object apply a 10N force on one end of the level's arm. Mar 1, 2020 at 13:16
• Related Post Mar 1, 2020 at 17:27

You are not just talking about forces and translation. You are dealing with a rigid body rotating, so you should use Newton's law for Rotation. As you said, $$\mathbf{\tau}=\mathbf{F}×\mathbf{r}$$.
$$\sum\mathbf{\tau}=I\mathbb{\alpha}$$ being $$I$$ the moment of inertia of the bar (which is $$1/12ML^2$$, for an homogeneous bar without the apples on it) and $$\mathbb{\alpha}$$ the angular acceleration of the bar (or the apples fixed on it).
In conclusion, don't think you have 2 forces, consider 1 torque. And, that's correct: with the same $$\sum\mathbf{\tau}$$ differents points on the bar move at a different $$||\mathbf{v}||$$.