a doubt regarding torque

dreamz25

If a body is rotating in a circular orbit then what is the moment of net force acting on it about the axis of rotation?

Doc Al

What do you think?

dreamz25

0 but how?

Doc Al

Which way does the net force act? What's the definition of torque?

dreamz25

in gravitation i have read that...
the force on a planet towards radius is given by
GMm/r^2
and the force which acts radially outwards is
Mv^2/r
so dunno where the net force acts... !!!:{
and torque = F X R
if the direction of net force is towards center then it makes and angle of
180 degrees which gives ex. torque = 0 as sin 180 = 0 ....
but just tell me about the direction of net external force...!! (Thanks in advance)

Doc Al

OK.
There is no outward force.
The only force acting is gravity.
Good.

dreamz25

How then do we derive the velocity of a plannet in circular orbit?????
when we equate both of them...
v = root[GM/R]...!!

Doc Al

By applying Newton's 2nd law. The only force is gravity. Set that equal to mass X the centripetal acceleration.

No need for any mysterious outward force.

dreamz25

ok.. so u mean both of them acts towards the centre... Right?
since the force on the particle by the center equals GMm/R^2
and also by Newton's second law of motion, F = ma so, F = m x centripetal acceleration (which is towards the center) = m x v^2/r
and thus we get, v = root[GM/r] ...?

cepheid

Your math is right, I think you just have a conceptual problem. When you say "both of them acts towards the centre", my question to you is, both of what?

We're not talking about two distinct forces here. Gravity IS the centripetal force in this situation. Centripetal force is always just a requirement for circular motion. It has to be provided by something real, like gravity, or tension in a string. Without something like this to provide (or act as) a centripetal force, there simply won't be any circular motion.

dreamz25

got ur point.... but i too meant the same...
i m nt differentiating the two force i just meant the different expressions for a single force..
the force between them is GMm/r^2 which also equals mv^2/r (the centripetal force which acts towards the center to keep the body rotating in a circular path) and thus gets the formula derived.....

dreamz25

wonderful lines... thanks..!!