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When you apply a force to an object, you are applying it to somewhere other than the center of mass since you cannot perfectly push it to the point. Centimeters, millimeters, micrometers---whatever it may be, it won't be the exact CoM (or whatever axis it may be). And when you apply a force to somewhere that is not the axis, you are applying a torque, which means it causes angular acceleration not linear. How is this possible? How are we able to move it linearly then? Do torques also cause linear acceleration? If so, is there some sort of mathematical formula?

(I feel like I missed some information on angular motion and stuff, I do not know what to google about this and all of them are not relevant)

Edit: I am asking this to simulate forces and torques in my computer. Please consider that I am ignoring the friction, air drag, how humans probably don't need to consider that, etc. etc.

arst10127402
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Usually this is because you are not pushing at a single point, or because there are other forces that contribute to the total torque.

You don't give any examples, but usually I don't push things with a force concentrated at a single point. I'll push a box with a splayed hand (or two hands). If one side were to move further, I would push less hard on it for it to stay in balance. I wouldn't try to push a large box with a stick because keeping it centered would be too difficult.

Also when I push a box on the floor, I don't have to worry too much about the vertical center. If I apply a small torque forward on the box, the weight of the box will cause the normal forces from the floor to shift so that the floor provides a counter-torque.

Do torques also cause linear acceleration?

A pure torque would not, but it's very difficult to find a pure torque on an object. An external force generally can apply a linear force and an angular torque simultaneously. Whether it causes a linear acceleration or an angular acceleration depends on what other forces are present.

BowlOfRed
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When you apply a force of 1N to the center of mass of a 1 kg object, the CoM accelerates 1 m/s^2.

When you apply a force of 1N to somewhere other then the center of mass of a 1 kg object, the CoM accelerates 1 m/s^2.

The acceleration of center of mass doesn't depend on where you are applying the force, because force is a flow of momentum, and the momentum has to be stored in the object, and stored momentum is calculated by multiplying mass with velocity of center of mass.

stuffu
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What I was really asking was if the distance from the axis mattered to linear acceleration as it is to angular acceleration when applying force. It does not. F=ma only cares about the magnitude of force and its direction, not its distance from the axis.

arst10127402
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