Let's say I hang an object of mass M from a string attached to the ceiling. The force of gravity on this object at rest would be [0,0,-Mg]. The tension force I assume would be [0,0,Mg] by Newton's third law. (Am I right on this?)(adsbygoogle = window.adsbygoogle || []).push({});

Next, assume I start the object spinning in a horizontal circle at a constant speed v. The force of gravity still points down, but the direction of the force of tension is now rotated. Let's say theta is the angle the end of the string (where the object is attached) makes with the horizontal axis, that the string is S meters long and that the circle the object is spinning has a constant radius R.

Now is where I start guessing, essentially. The magnitude of the tension force would be (Mv^2)/R (by using Newton's second law and the fact that for uniform circ. motion the acceleration a = (v^2)/R). The vector of the tension force would be (Mv^2)/R multiplied by [cos(theta),sin(theta),0]. Is this right?

Any help would be greatly appreciated. Thank you!

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# Tension of string and circular motion question

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