Examine(adsbygoogle = window.adsbygoogle || []).push({}); T=rxF(cross product),

where |T|=|r||F| sin t, where t is the angle betweenrandF

The intuitive idea of torque (let's only consider torque about the pivot for now) is that the stronger the force or the further away you are from the pivot point, the more the object will TEND to rotate.

The cross product formula above does match this intuitive idea. For example, larger force, the magnitude of the torque really does increase. It also matches the observation that no torque is generated when t is zero, and max torque when t is at a 90 degree angle.

My question is, what about the angles in between? Using the formula, does this really match with what nature is telling us? Does the formula truly reflect the intuitive idea of torque in terms of the tendency of making an object rotate? I don’t see a reason why it has to obey the sine relationship/curve other than the fact that at t =0 and t=90 we see min and max respectively. For example, why can't it be a linear relationship for angles in between?

Thanks!

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# Why is Torque the Cross Product Between r and F?

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