After detecting a collision between two convex shapes by using separating axis theorem and calculating MTV. How can I calculate the contact points?(for applying torque to the rigid body).
29264
The Separating Axis Theorem (SAT) makes it simple to determine the Minimum Translation Vector, i.e., the shortest vector that can separate two colliding objects. However, what I need is the vector that separates the objects along the vector that the penetrating object is moving (i.e. the contact point).  I drew a picture to help clarify. There is one box, moving from the before to the after position. In its after position, it intersects the grey polygon. SAT can easily return the MTV, which is the red vector. I am looking to calculate the blue vector.    My current solution performs a binary search between the before and after positions until the length of the blue vector is known to a certain threshold. It works but it's a very expensive calculation since the collision between shapes needs to be recalculated every loop.  Is there a simpler and/or more efficient way to find the contact point vector?
115345
If I have two metal rods arranged like a ramp with coefficient of friction $\mu$, at an angle $\theta$ to the ground, and a solid metal ball or radius $r$ and mass $m$ rolling down between the two tracks in such a way that it touches both of them, how does the separation between the tracks $d$ affect the acceleration $a$ of the ball, assuming a uniform gravitational field of strength $g$?  I know that I can model a box sliding down a ramp using equations with energy but how do I calculate for a rolling ball, and take into account the separation between the tracks?
84076
I don't know how to name what I am searching for... Force, Impact? It's easier to explain with an image for me. We have two GameObjects with colliders, A and B. They can move in any direction (top down game with 360° movement possibilities). First case (left): A go to the right at a speed of 2, B to the left at a speed of 1 and they collide. How to calculate that A take 1 damage (from the speed of B in its direction) and B take 2. Second case: A go to the right at speed of 2 and B to the right at speed of 1. A take 0 damage and B take 1.    I am using Collision2D which doesn't have "impulse" property. I have no idea how to calculate thing like this manually.
8663
I am writing a breakout clone (my first game) and am totally stuck as to how I figure out which side of the brick was hit.  I have a collision detection method that looks like this:  DetectCollision(Object a, Object b)     x = distance(a.x, b.x);    y = distance(a.y, b.y);     if (x is smaller than the combined width &amp;  y is smaller is than combined height {        return true;    } return false;     This works totally fine, but I need to know the side of the collision, and location relative to the center in order to respond properly.  I've spent the past few days snooping around but am lost.
38481
In my book, the following are described to be the steps that one must follow if he wishes to find the direction of static friction force acting on an object:  &quot;(1) Draw the F.B.D(free body diagram) of the object in question with respect to the other object on which it is kept. (2) Include the pseudo force also, if the contact surface is accelerating. (3) Decide the direction of the resultant force and resolve this force into two components; one along the surface of contact and the other along the normal to this surface. (4) The direction of static friction is opposite to the component of the result force along the contact surface.&quot;  Firstly, are these steps correct? Will I always obtain the correct answer by following these steps? Secondly, consider the following problem:  In questions like these, when I try to find the resultant force and then assign the direction to static friction, I find that my answer is incorrect! Are there some other steps to follow when I know that the object is definitely accelerating in one direction or another? Edit 1: I approached the above question by doing exactly what my book suggests; first, I identified all the forces acting on the smaller block, being the normal force applied by the block A and its weight mg downward. Adding these two forces, I get another force that actually acts on the body like so:  I wonder if I'm not supposed to take either of the contact forces into consideration when drawing the F.B.D to figure out the direction of static friction acting on the body. Also, are there other steps for finding the direction of kinetic friction? Edit 2: From Judge's answer, I have been able to figure out my mistake, it being that I completely missed step (3) and didn't resolve the resultant force into components! Sheesh. Sorry! Much thanks in advance! :) Regards.
10008
I ve tried to solve this problem in so many ways but still didn't manage to do it...    What would be the correct way to solve it please?  This arm of this mechanism has a length of 0,2m. The piston has an angular velocity of 2000 tours/min clockwise. What would be the velocity of point D for an angle theta of 60 degrees?  I think that what I am missing is the angle formed by the arm and the line, which is 50mm long. Example like here (different  exercise):    I am trying to look for this angle beta which could help me solve the problem. A little bit more than just a formula as a hint would be great!  I am new to mechanics so a manner to solve this problem, which is similar to the example given (gemetrically), would be nice.  expected answer:2,88m/s
73565
Question Consider two dipoles $({p_1}\hat{i}$ and ${-p_2}\hat{j})$ kept in the $x-y$ plane at $(0,0)$ and $(d,0)$ respectively. Calculate the torque about the COM. Approach 1 Suppose we select the COM as the origin. Then, we label the 4 particles $1,2,3,4$. Let their position vectors be  $r_{1},r_{2}..etc$. Then, when we consider the Force on the $i$th particle due to the $j$th particle= $F_{ij}$. The Torque about the COM.= $r_{i}\times F_{ij}$. When we sum these torques over all particles, and use the following facts:  $F_{ji}=-F_{ij}$ $r_{i}-r{j}=r_{ij}$ $r_{ij}\times F_{ij}=0$  $$r_{1}\times({F_{21}+F_{31}+F_{41})}+r_{2}\times({F_{12}+F_{32}+F_{42})}$$ $$+r_{3}\times({F_{13}+F_{23}+F_{43})}+r_{4}\times({F_{14}+F_{24}+F_{34})}$$ $$= (r_{1}-r_{2})\times F_{12}+(r_{1}-r_{3})\times F_{13} ....$$ $$=0 + 0 ...0$$ We conclude that the net Torque about the COM is is zero. This is somewhat expected, there are no &quot;external&quot; elements in our system. (In fact, this argument suggests that the Torque about any point in the x-y plane is zero. We will still end up with the same expression, as the difference of two position vectors is independent of the choice of the origin.) Approach 2 However, qualitatively, when we use our knowledge of electric fields, we can see that both dipoles seem to experience an anticlockwise torque. They will add up, and thus The net torque is non zero. This appears to be a contradiction. The latter finding is bizarre in the sense that it seems to suggest that the angular momentum of an isolated system is not constant. And the only way that argument 1 can be wrong , is if: $$F_{ij}=-F_{ji}$$ does not hold. I have seen this happen, but the explanation was that the &quot;3rd law of motion&quot; is actually a statement of the conservation of momentum, and in that particular case, some portion of the momentum (of the particles) was carried away by the associated electromagnetic field. I don't think that something of this sort is responsible for my particular case, since there is no $B$ field, and therefore no $S$, which appears in the momentum density of the fields. Apart from this, the two arguments seem to be quite valid individually. So what's going on here? My initial thought was that the fields might be storing angular momentum, but like I said, there is no $B$. Edit 1: I think I have a hypothesis: In approach 2, as the dipoles rotate for some time say $dt$ , they start producing a $B$ field (since we now have moving charges). We now have both $E$ and $B$ fields, so we actually have an angular momentum associated with the field, which perhaps cancels out with the angular momentum produced by the dipoles(=$(T1 +T2)dt$).
83781
I'm building a physics simulator for a graphics course, and so far I have it implementing gravitational and Coulomb forces. I want to add collisions next, but I'm not exactly sure how to go about doing it.   A quick summary of how this is working so far is: All objects are spheres of a set radius, mass and charge. The mass's and charges of the spheres are treated as point charge/mass for the calculation. Every step in time (about 1/50th of a second) the forces acting on each object are calculated in a nice big nested for loop that figures out the coloumb and gravitational force between 2 objects, for every set of 2 objects, and then they are summed together. I use this net force to determine the acceleration, and the rest is fairly obvious from there.   What I want to add in is collisions. I can deteremine pretty easily if a collision is happening (if the distance between them &lt;= radius of one + radius of other), what I am not so certain of is how I should add in the collision force (and would need to do it component wise). I want elastic collisions, though for now I'd just be happy with getting conservation of momentum  The information I have easily available are: the velocity of each object (and I mean velocity, speed and direction), the position of each object, the mass/charge (charge obviously not needed here) and the Net force calculated so far for each object for the next step in time. I dont need exact formulas (would prefer if they arent exact), just need a nudge in the right direction.
8725
Suppose an object of mass $m$ starts at rest at a radial distance $ r_0$ from a perfectly spherical mass $M$ (where $m &lt;&lt; M$), $r_0 &gt; R =$ radius of $M$.    Can we analytically determine when $m$ will hit the surface of the $M$?  In other words, can we analytically solve this initial value problem:  $$ \frac{d^2r}{dt^2} ~=~ - \frac{GM}{r^2} ,$$ $$ \dot{r}(0) ~=~ 0 ,$$ $$ r(0) ~=~ r_0? $$
49573
How can I tell whether a circle and a rectangle intersect in 2D Euclidean space? (i.e. classic 2D geometry)
26772
I have an intuition problem  calculating torque using the cross product formula.  As for example let the magnitude of the force be 50 lbs and length of the  wrench be one foot and you are exerting force in a clockwise motion and the angle you apply the force 60 degrees.  This is an example so I can ask my question.  Using the right hand rule the torque points  perpendicular to the force you are applying to the bolt. In this case since the sine of 60 degrees is about .86 it would be (.86)(50) foot lbs. How can the bolt turn clockwise if the force is concentrated perpendicular to where it needs to turn?  The cross product formula demands the torque be perpendicular. Obviously my mistake but I don't see where.
123462
For a long time I have wondered if there is a way to show that the rotational analogs of Newton's Laws are a direct consequence of just those laws, or are we adding more to them?  I understand mathematically that we take Newton's second law and do "r cross both sides," but that has always struck me as using more than just the 2nd law.  Here it matters where forces on the body are applied, but I don't see where Newton's Laws talk about points where forces are applied to a body. For translational motion it doesn't matter.  So are we adding a sort of "extra law" when we do this for rotation?  The only thing I can think of would be to "disassemble" an extended body into differential point masses and work with internal constraint forces that make the body rigid. If every mass is just a point mass it would get around the issue I'm having.  I've never seen any discussion along those lines, though.
25420
When two bodies, free of movement, are linked by a physical constraint (a maximum distance between them) how do their masses and velocities influence each other? Which formula with theses parameters gives the force applied by one of the two on the other?  For example : I have two box (grey and red) that are next to each other attached by a rope of maximum length L, the grey one jump following the yellow curve C and i'm trying to get the equation to find the force applied to the red box when the distance between the boxes reach L. V is the velocity when the gray box reach the red circle. It would probably split into the radial force and the tangential force depending on the angle. I guess the answer would probably work for every position on the red circle.  I tried to read about pendulum but there was only the gravity taken into consideration, and it kinda felt like the tension was vertical. There might be an answer for me in one ticket but i just couldn't find it.
33798
The  characterizes a collision in one dimension by relating the initial and final speeds of the particles involved,  $$C_R = -\frac{v_{2f} - v_{1f}}{v_{2i} - v_{1i}}$$   In a 2D collision, the velocity can be split into components parallel and perpendicular to the "plane of collision" (the plane tangent to the two objects' surfaces at their contact point), and the equation above applies to the perpendicular components of the velocities only. One could write  $$\begin{pmatrix}v_{2f\shortparallel} - v_{1f\shortparallel} \\ v_{2f\perp} - v_{1f\perp}\end{pmatrix} = \begin{pmatrix}1 &amp; 0 \\ 0 &amp; -C_R\end{pmatrix}\begin{pmatrix}v_{2i\shortparallel} - v_{1i\shortparallel} \\ v_{2i\perp} - v_{1i\perp}\end{pmatrix}$$   My question is, is it useful (i.e. does it produce a more accurate description of realistic 2D collisions) to generalize that matrix? Perhaps by allowing the top left element to be unequal to 1, or allowing nonzero off-diagonal elements? Or is there some nonlinear relation that works better?  As usual, if you know of any relevant published research, references would be much appreciated.
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.
84209
I'm developing a 2D game including collisions between many disks. I would like to know how I can get the angle corresponding to the new direction of each disk.  For every disk I have this information : direction (integer), speed (float), and position ($x$;$y$, which are both integers).  Of course I know that the new direction will be the opposite of where the collision happens (disk hit on the bottom-left will go to the top-right), but I don't know how to calculate exactly the new angle.
21997
I am having some issues with trying to detect collision of two isometric tile.  I have tried plotting the lines between each point on the tile and then checking for line intercepts however that didn't work (probably due to incorrect formula)  After looking into this for awhile today I believe I am thinking to much into it and there must be a easier way.  I am not looking for code just some advise on the best way to achieve detection of overlap