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# Physics/Dynamics of rigid bodies - linear and rotational

Question
If we apply a force to any object say a rod at its very end, in space, will it translate or rotate or both as viewed from a frame of reference from which it was initially at rest. shouldn't it only translate as the resultant of all the force on a body is what accelerates the centre of mass and since there is only 1 force it must accelerate centre of mass accordng to f=ma. if this is true would it not be true that 2 forces are always required for rotation? and if it isnt true and the body also rotates, then what decides what shall be the angular acceleration produced and what shall be the acceleration of COM?

> would it not be true that 2 forces are always required for rotation?

No.
Think of this example (I hope you've played volleyball).
Imagine you're holding a volleyball in your hand, getting ready to serve it. You not only want to accelerate it over the net, you also want to put some spin on it. Thus, you apply a force on it (with your other hand) on the side of the ball, but still give it enough force to send it over the net. These images
http://bba.volleyball.free.fr/serveffet.gif
http://www.austinvolleyball.com/images/serve2-6.jpg
http://www.real-world-physics-problems.com/images/magnus_effect_volleyball.png
should give you and idea on what you are doing, and why you do so.

There's only one hand hitting the ball, thus only one force on the ball. Nevertheless, the ball accelerates towards the net AND spins as it does so. Even after only one force has been imposed on it.

It's not unlike taking an object and imposing a force on it, whose direction is not perfectly in either the x-axis or the y-axis. What we do is break up the force into each of its components along each axis, and then calculate what happens along each axis. One force, two components (one component along the x-axis, the other along the y-axis). Similarly, we can take that one force on the rigid body and divide it the linear acceleration force and the torque force.

"Okay," you may ask, "how do we calculate how much the ball accelerates in linear motion and how much it begins to spin?" The answer, unfortunately, is that there is no easy way to do so. It's relatively easy to calculate what happens to the center of mass of an object when a force is imposed on it. It's also relatively easy to calculate what happens when a torque is imposed on a rigid body that remains motionless. To do BOTH gets quite a bit more complicated.

The best place to start is
http://emweb.unl.edu/NEGAHBAN/EM373/note19/note19.htm
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