When an impulsive force is acted upon a rigid body, (and the force doesn't pass through the centre of mass) why does the body rotates specifically about an axis passing through centre of mass ?
98799
If a force is applied to a body which does not act through its centre of mass, it rotates about its centre of mass and not any other point. Why?
14453
If some object is kept in a radial groove made on a disk and the disk is rotated with say constant angular velocity.   Now as we know that the object moves outwards ie away from the centre of the disk. I want to know which force is it which throws the object outwards.   As centrifugal force is a pseudo force and hence when the observer is in ground frame it shouldn't be present so which force exactly pulls it out.
80356
There is a ball rolling down an incline, with no slipping. If we consider the point of contact between the ball and the inclined plane to be the pivot point (for our torque calculations), then I have noticed that friction is no longer in play, and gravity (and normal force) is the reason for the torque. However, if we consider the center of mass of the ball to be the pivot point, friction is the only factor, since both the normal force and gravity effect the center of mass (so the net torque caused by them is 0, since the pivot is the center of mass). However, both of these produce different torques.. for different reasons. So my question is,   Is gravity the reason a ball rolls, or is friction? And why?  [Note: This is not homework, it is a genuine question I had while looking at some physics problems.]
15882
As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong.
51933
The definition of  is  "Inertia is the resistance offered by the body whenever its state of motion is changed."   What is inertia of a body? Is inertia actually a force exerted by the body?  If so, then why is there no application of inertia in numerical problems involving application of force on a body? What is the actual application of inertia in theory?
45032
If I push or hit an object in space (vacuum and no gravitation) in direction what is not going trough its centroid, will it rotate or move along in straight line?   I expect that on earth it will depend on what is less difficult for the object (rotation or linear movement). So the object will do some kind of combination of both movements (rotating and also moving along the direction of impulse or force).  But how could an object "decide" what to do in space, where is not resistance?
4134
Let us say a block of mass is placed on the surface of earth. Then while drawing the forces on that body, we say:   Force $F = mg$ acting towards the center of Earth. Normal reaction $N$ offered by the surface of Earth.   If no other forces are acting, we say $F=N$. But what about the centrifugal force $m\omega^2R$ . Why don't we ever bring that into picture? What am I missing?
123572
Problem #25 from the 2009 $F=ma$ contest:     Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on the rods. The discs have identical thickness and are made of the same material, but have differing radii $r_1$ and $r_2$. The discs are given angular velocities of magnitudes $\omega_1$ and $\omega_2$, respectively, and brought into contact at their edges. After the discs interact via friction it is found that both discs come exactly to a halt. Which of the following must hold? [...] Ignore effects associated with the vertical rods.   Diagram here:     Probably conservation of angular momentum is useful here, but I am not clear how it can be applied. There are two distinct axes of rotation, one for each disc, so we cannot talk about conservation of angular momentum about one axis. If the two disks rotated about the same axes then the solution is straightforward, but this is not the case.
94446
In most of the cases the center of mass is chosen for rigid body motion description, but this is not an obliged choice, since the motion of any point $P$ of the rigid body can be seen as the combination of a traslation of another point $Q$ and a rotation about an axis passing through $Q$. I'm trying to understand what are the main reason why the center of mass is  chosen as the origin for the frame of reference in rigid body dynamics.  I thought about these main reasons:   Center of mass theorem: $\sum F^{(external)}=M a_{CM}$. Nevertheless this concerns traslation motion only and the traslational velocities of the points of the rigid body are all the same, so in principle I could write $\sum F^{(external)}=Ma_{P}$, where $P$ is a random point of the rigid body. Does that makes sense? Koenig theorems (kinetic energy and angular momentum) Parallel axis theorem   The last two, as far as I understood, are valid only if the center of mass frame is used and in no other case. Is it correct?  Are these the main reason why the center of mass frame is used in rigid body dynamics, or are there other reason behind this choice?
65676
Consider a cylinder that rolls without sliding on an inclined plane. If it's placed at the top of the plane, with its center of mass at a height $h$ from the bottom, it will have a potential energy $mgh$ (considering the bottom of the plane as the zero point). Then, the cylinder will start rolling down the plane, as its weight does work on it, causing its potential energy to be transformed into rotational and translational kinetic energy. I'm confused about the origin of the rotational kinetic energy of the cylinder. Since the static friction and the normal force are applied at the point of contact with the plane, neither of them can do work on the cylinder (which is why its mechanical energy is conserved), since the cylinder is, by constraint, not sliding. This seems to imply that the cylinder's rotational kinetic energy comes from the work done by its weight. However, I don't understand how this happens, since a rigid body's weight can be seen as being applied on its center of mass, which means it can exert no torque on it. Instead, the only torque exerted with respect to its center of mass comes from static friction. Moreover, if the inclined plane was frictionless, there would be no torque exerted on the cylinder, so it would not rotate. Yet, I don't see how this situation could be distinguished from the previous one by only looking at the cylinder's mechanical energy (since the normal force would still be doing no work). So, my question is: how is gravitational potential energy converted into rotational kinetic energy, and what is friction's role on this?
70844
I found after searching that this question has been asked before. But all the answers were not convincing. Suppose I have a body which is free, not constrained always rotate about its center of mass (COM). Why is that so? A convincing answer that I found was that in most cases the moment of inertial about the center of mass is the least and that's why the body rotates about the center of mass. But I ask it again with hope of the question not getting closed and getting a better succinct answer. I was thinking that motion about the COM is the most stable one and the rotation about other points degenerates. I don't think it's right. Is it? —————————————————————————————————— Note-: 1). This question has been wrongly closed. The other questions linked don’t answer my question at all. It asks me to ask a new question if my question is still not resolved. I did make it clear that I am not satisfied with the answers in the linked questions. 2). The answer to this question is that a free body never rotates about its center of mass ( the instantaneous axis of rotation never passes through the center of mass). In fact we choose a point about which we want to decompose the motion into rotation and translation and we could very well have chosen any point other than the center of mass and analysed rotation about it. Moreover the instantaneous axis of rotation for a free body never passes through the center of mass. I would urge the moderators to give me the right to add my answer to this question. This is the correct answer, the one which satisfied me the most and it is nowhere in the linked answers. So kindly give me the right to open this question and let me add my answer to it.
54091
I struggle to find a satisfying reason and formulation, why for a point mass,  that is fixed in a rotational system and the radius is changed (like pulling on a string with a small ball rotating around it), the speed of this point mass would increase due to the conservation of angular momentum.  that follows a trajectory with decreasing radius (like a Roller Coaster on a Spiral shaped rail), the speed of this point mass would not increase, since conservation of angular momentum is not applicable in this case. (I already started doubting, if it really does not increase).   The only reason I found so far is that in the second case, the rail acts as an external force to the mass, while in the first case the radius change is an internal change of the system that comes along with putting energy into the system by working against the centrifugal forces. While I expect this is a somewhat correct answer, I still find this is a little bit hand waving argument. I expect that I just miss a proper clean definition of external force vs internal force. I also constructed the following thought experiment for myself, that involves an external rail, but I would expect to react like the first case: When a point mass rotates on a circular stretchable rail and the radius of that rail would be changed by applying some force against the centrifugal force of the point mass, I'd also expect the velocity of the point mass increases, since some force applied over a distance (energy change) is involved. But I doubt that the applied force over a distance is the underlying fundamental reason and I expect that there is another more satisfying fundamental difference between the fixed predetermined trajectory and the thought experiment / the first case mentioned in the beginning.
32024
From  follows that, given a rigid body, the moment of inertia is minimum if calculated with respect to an axis passing through the center of mass. What is the physical meaning of this?   The moment of inertia plays the role of the mass on rotational motion, so it is linked to the reluctance of the body to rotate. Given a torque, if the axis passes through the CM the angular acceleration is maximum, while it decreases increasing the distance from CM. Why does that happen?  I tried to justify it as a consequence of the distribution of mass around the CM, but I do not know if that is right.
93209
For a long time, I have been thinking about this: In order to stop a moving body, I have to apply impulse to change the existing momentum to $0$. For the impulse I have to impart force on the moving body . That means I have to eliminate all the kinetic energy associated with the moving object in order to bring it to a halt. Thus, work is done on the object, right? If work is done, energy must be given by me...  Here is where my confusion arises:   If I eliminate the associated kinetic energy of the body, where does this energy go? The work(?) done by me on the moving object to stop it obviously uses energy from me. Again, where does this energy go?
75939
A mass of point performs an effectively 1-dimensional motion in the radial coordinate. If we use the conservation of angular momentum, the centrifugal potential should be added to the original one.     The equation of motion can be obtained also from the Lagrangian. if we substitute, however, the conserved angular momentum herein then the centrifugal potential arises with the opposite sign. So if we naively apply the Euler-Lagrange equation then the centrifugal force appears with the wrong sign in the equations of motion.   I don't know how to resolve this "paradox".
38054
A body continues in its state of motion unless a force is applied to it. But how does an object stay in motion in the first place? A force must have caused it to move right?
97375
When an object is moving in a circle, won't the frictional force oppose it's motion? And if the velocity is always tangential to the path, there is no component of it towards the center, so there is no component of friction towards the center (since the frictional force is antiparallel). So how can friction be a centripetal force, like in the case of a car rounding a corner?