Conversation started Nov 21, 2022 at 11:29.
Wolgwang
Wolgwang
Nov 21, 2022 11:29
@JohnRennie If we apply force at COM, then there is no rotational motion but if we observe wrt to some other point there is a torque. How do we resolve this inconsistency?
John Rennie
John Rennie
@123 They are basically the same thing.
123
123
@JohnRennie How ??? It looks me same also.
In law of conservation of momentum we isolate the object from all external forces.
John Rennie
John Rennie
@Wolgwang It isn't an inconsistency, because if we take some other point and calculate ω and α we would find that for that other point α ≠ 0.
Wolgwang
Wolgwang
@JohnRennie So it is just like frame? (Rotational motion in one frame and not in other)
123
123
$\sum F_{Ext} = \frac{\Delta{P}}{t}$ Which is newton's second law. If $\sum F_{Ext} = 0$ then $\sum P_i = \sum P_f$.
John Rennie
John Rennie
Nov 21, 2022 11:35
@Wolgwang I can draw a diagram if you want ...
Wolgwang
Wolgwang
@JohnRennie Hmm @123 Can I ask JRS doubt first? I believe it won't take much time?
123
123
$\sum F_{Ext} = \frac{\Delta{P}}{t}$ Which is newton's second law. If $\sum F_{Ext} = 0$ then $\sum P_i = \sum P_f$. This derived from newton's second law. And newton's 1st and 2nd law are response of single object , but newton's third law act on different objects.
@Wolgwang Sure....
Wolgwang
Wolgwang
Thanks
John Rennie
John Rennie
user image
If we consider just the object it accelerates at a = F/m i.e. just regular Newton's laws, and it doesn't rotate because there is no torque on it. Yes?
Wolgwang
Wolgwang
Yes
John Rennie
John Rennie
Nov 21, 2022 11:41
Now if take the point P as our reference there is a torque τ = Fx, so there should be an angular acceleration α = τ/I. Yes?
Wolgwang
Wolgwang
@JohnRennie Yes
John Rennie
John Rennie
If we assume the sphere is small the moment of inertia is I = mx². If we aren't allowed to assume it's small then we'd have to take I for a sphere and use the parallel axis theorem, which would get a bit involved, so let's just assume the sphere is small. OK so far?
123
123
@JohnRennie If you have time pls answer my question.
Wolgwang
Wolgwang
@JohnRennie Ok
John Rennie
John Rennie
So α = τ/I = Fx/(mx²) = F/mx.
Yes?
Wolgwang
Wolgwang
Nov 21, 2022 11:45
Yes
John Rennie
John Rennie
Now considering just the sphere we have the usual Newton's second law a = F/m.
Wolgwang
Wolgwang
Yes
John Rennie
John Rennie
And for any system the linear and angular accelerations are related by a = rα. Yes?
Wolgwang
Wolgwang
Yes
John Rennie
John Rennie
So we get a = F/m = rα = x (F/mx)
Yes?
Wolgwang
Wolgwang
Nov 21, 2022 11:48
Yup
John Rennie
John Rennie
And we end up with F/m = F/m
which is true :-)
Wolgwang
Wolgwang
Makes sense. Thanks :)
John Rennie
John Rennie
So the point is that working with the linear forces using Newton's second law gives exactly the same as working with angular quantities.
It's just two different ways of describing the same motion.
 
Conversation ended Nov 21, 2022 at 11:50.