According to Newton's Laws of Motion if the net force is zero then the object does not undergo and change in motion or direction. But how when net force is zero, body initially is at rest and torque is not zero, rotational motion is possible? i.e. net force is zero but how is rotational motion possible.
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4$\begingroup$ According to Newton's Laws of Motion, if the net force is zero, then the object does not change its linear motion or its direction thereof. A non-zero net torque but zero force is fully allowed to have rotational motion in accordance with the above. $\endgroup$– naturallyInconsistentCommented Mar 26 at 7:54
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6 Answers
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According to Newton's Laws of Motion if the net force is zero then the object does not undergo and change in motion or direction
Actually, Newton's first law, as apparently stated by Newton himself, does not specifically state a net force of zero. According to an article in The Scientific American (link below) what Newton actually said was the following:
"Every body preserves in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by the forces impressed."
The article discusses a misinterpretation of the law. And while the misinterpretation does not specifically involve rotational motion, it has been suggested a better paraphrase of the law to reflect Newton's original intent would be the following:
"Every change in a body's state of motion is due to impressed forces"
Note that the phrase 'body's state of motion' allows for both rotational and translational motion. And the term "impressed forces" allows for the possibility of change in rotational motion due to equal and opposite parallel non collinear forces where the net force is zero, but the net torque is not. Such a system of forces is referred to as a "force couple" or simply a "couple'. A couple causes pure rotational motion without translational motion.
Hope this helps.
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Imagine pushing on a plate from either side. It doesn't move because of Newton's 1st law - the two forces are equal but opposite and cancel out. More precisely we would say that it doesn't translate (linear motion) and it doesn't rotate (angular motion). It is stationary
But now offset the two forces slightly so that they are both pushing slightly to the side from the centre. The object experiences the exact same forces as before, just not at the same point. The object thus still won't translate (no linear motion), but it obviously will start spinning around about it's own centre (non-zero angular motion).
This shows us that there is a distinction between the two types of motion. Newton's laws of motion with respect to forces tell us how the object moves linearly. E.g. in simple formulas, the first law is $\sum F=0$, the second law is $\sum F=ma$, and the third law is $F_{ab}=F_{ba}$. You can derive Newton's equivalent laws of rotational motion, which would be $\sum\tau=0$, $\sum\tau=I\alpha$, and $\tau_{ab}=\tau_{ba}$, respectively.
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$\begingroup$ So, does newtons law apply separately for translational and rotational motion? And does newtons laws apply only for translational motion? $\endgroup$ Commented Mar 26 at 8:02
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net force is zero...how is rotational motion possible?
Imagine a rock that somehow has been hurled out into the void between galaxies. Its center of mass is moving at a practically constant velocity (i.e., it does not feel significant "net" gravitational force from the distant galaxies that pull on it from many different directions) and, it is slowly rotating.
How can it be rotating? Does that not mean that individual atoms of the rock are continuously accelerated? How can the atoms be accelerated if they experience no net force?
The answer is that individual atoms do feel net force. They are "bonded" to one another by the action of their electrons. Without those bonds, the rock would turn into an expanding disk of gas. Each of its atoms would fly off in a different direction at a different speed, and follow its own, unaccelerated path.
The rock as a whole feels no net external force, but it is the internal forces (a.k.a., "stress") holding it together that give it the ability to rotate. Each atom feels a net "centrifugal" force that keeps it revolving around the rock's center of mass.
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If the net force on an object is zero then the motion of its centre of mass is unchanged i.e. its centre of mass will continue to be either at rest or moving in a straight line with constant speed.
However, if there are external forces on the object that do not act through its centre of mass then they can create a couple about the centre of mass, and a non-zero torque from this couple will change the object's angular momentum about its centre of mass.
A similar effect is observed without any external force if a rotating object reconfigures itself by moving parts of itself closer to or further from its centre of mass. In this case the object's angular momentum is conserved (as long as there are no external forces) but its angular speed will change if its moment of inertia changes.
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According to Newton's 2nd law, net force only describes the change in momentum of an object. Momentum is defined from the translational velocity of the center of mass, and thus net force is related to changes in the translational velocity of a body.
Hence
$$ \vec{F}_{\rm net} = m \, \vec{a}_{\rm com} \tag{1} $$
where $\vec{F}_{\rm net}$ is the net force acting on the body, and $\vec{a}_{\rm com}$ the translational acceleration of the center of mass (specifically).
When considering a rigid body as a finite collection of particles that are stuck together then you will discover the rotational form Newton's law (also known as Euler's law of motion) as
$$ \vec{\tau}_{\rm net, com} = {\rm I}_{\rm com}\, \vec{\alpha} + \vec{\omega} \times ( {\rm I}_{\rm com} \vec{\omega}) \tag{2} $$
where $\vec{\tau}_{\rm net, com}$ is the net torque acting on the body about the center of mass, ${\rm I}_{\rm com}$ is the mass moment of inertia (tensor) of the body about the center of mass, and $\vec{\alpha}$ is the rotational acceleration of the body.
There are cases where $\vec{F}_{\rm net}=0$, but the net torque is not zero. This is a case of a pure torque applied and it is often labeled as a force-couple where two equal and opposite forces are acting on the same body, but at some offset distance between them (their lines of action).
It is physically difficult to actually apply a pure torque, but mathematically it is convenient to simplify things to just a torque when the action of the applied forces are not important.
answered Mar 26 at 14:08
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A rock is a rigid body. Its atoms exert forces on each other in such a way as to keep distances and angles between them unchanged. These are called internal forces, because they are forces between parts of the rock, not on external objects.
Newton's laws say that forces always come in equal and opposite pairs. If atom 1 exerts a force on atom2, the atom 2 exerts an equal and opposite force on atom 1. This means the total of all the internal forces add to $0$.
Never the less, the total force on atom 1 or atom 2 may not be $0$.
If the rock is rotating, each atom follows a circular path. The total force required to keep an atom following a circle instead of a line is a force directed toward the center of the circle. This is called centripetal force. You can see how these forces can add up to $0$.
An external force is a force on the rock from an external object. If you push on one atom, that atom pushes on its neighbors, and they push on other atoms, and so on. So all the atoms are affected by the force. This does accelerate the rock.
The simplest case is where there is no rotation. All the atoms have the same acceleration and the same velocity. It makes sense to talk about this as the acceleration and velocity of the rock.
Suppose we push on a rock for a while and then let it move freely. If there is rotation, all the atoms follow circular paths around an axis. The axis may move. The velocity of the rock can be described as the velocity of the axis.
For more, see Toppling of a cylinder on a block
