 #1
LCSphysicist
 634
 153
 Homework Statement:
 Actually is a conceptual doubt
 Relevant Equations:

L = Iw
T = rf
g = g
I was always a little confused about the rolling down of a body, let's say, a sphere.
It's know that to body rotate, from the rest, in a referential frame on the ground [inertial], is necessary a friction, that will just act like a medium that transforms kinetic energy of translation into rotation.
I want to justify this, because if we take a torque about the point of contact, will the weight the producing force of such, and this can make a confusion i guess. I will try justify to myself to clarify the ideas and would like that you help me.
So about the contact point, the weight will produce a torque T = (rmgsiny)k^. We know too that the angular momentum about that point is (Ip*w)k, Ip relative to this point [not to center of mass]
But, T = L', so
r*m*g*siny = Ip*a(alpha)
Well, the point is, w is not constant, this is where i think that confused me, i need to clarify once and for all this point.
a is not constant RELATIVE to the point, it doesn't the same thing to say that the body will rotate, since we know that the instantaneous w of a point is equal to v/d (d relative a point), if the v varies, w will to, not about rotation ordinary.
Now, analyzing by the center of mass, we have L = Io*w, if w is constant we could stop, assume that w varies.
So L will varies to, but, if we analyze all the forces in the body, immediately we could say:
There is a Normal, and a Weight force, passing the center that produce no torque.
Assuming the resistive force of the air nonexist, and the body as rigid, the only force here to make it varies is the friction.
Now we know that the friction produce the torque, so route about the center of mass, which is the only relative motion possible to a particle on the body.
That's the "true" rotation that we always says.
Is this right?
It's know that to body rotate, from the rest, in a referential frame on the ground [inertial], is necessary a friction, that will just act like a medium that transforms kinetic energy of translation into rotation.
I want to justify this, because if we take a torque about the point of contact, will the weight the producing force of such, and this can make a confusion i guess. I will try justify to myself to clarify the ideas and would like that you help me.
So about the contact point, the weight will produce a torque T = (rmgsiny)k^. We know too that the angular momentum about that point is (Ip*w)k, Ip relative to this point [not to center of mass]
But, T = L', so
r*m*g*siny = Ip*a(alpha)
Well, the point is, w is not constant, this is where i think that confused me, i need to clarify once and for all this point.
a is not constant RELATIVE to the point, it doesn't the same thing to say that the body will rotate, since we know that the instantaneous w of a point is equal to v/d (d relative a point), if the v varies, w will to, not about rotation ordinary.
Now, analyzing by the center of mass, we have L = Io*w, if w is constant we could stop, assume that w varies.
So L will varies to, but, if we analyze all the forces in the body, immediately we could say:
There is a Normal, and a Weight force, passing the center that produce no torque.
Assuming the resistive force of the air nonexist, and the body as rigid, the only force here to make it varies is the friction.
Now we know that the friction produce the torque, so route about the center of mass, which is the only relative motion possible to a particle on the body.
That's the "true" rotation that we always says.
Is this right?
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