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  1. K

    Magnetic energy density, and pressure due to magnetic force

    Hi Steven, I meant to say that the answer of 318 Pa using ilB seems right to me
  2. K

    Electric field in a rotating rod in a magnetic field

    @above as otherwise the lorentz force would exceed the centripetal force
  3. K

    Electric field in a rotating rod in a magnetic field

    The first part of the problem seems easy enough, the free electrons in the wire would move in a circle owing to an electric field that would be induced in the rod which would provide the centripetal force for the same (Please correct me if I am wrong). So we have $$eE=mω^2x$$, where e is the...
  4. K

    Magnetic energy density, and pressure due to magnetic force

    Here's a perspective on it: consider a hollow cylinder with a current flowing along its length, now consider a small element on this cylinder. It's easy to see that it would experience a force due to the other elements on the same wire. I like to think of this as a small element (which is...
  5. K

    Tyres of a car lifting when turning left sharply....

    Can't we use basic centrifugal force for this? My professor told me to think along these lines (we haven't done torque yet) and I just believe that I over complicated my explanation a bit, and that a centrifugal force is pushing the car outside.
  6. K

    Tyres of a car lifting when turning left sharply....

    Homework Statement Why do the left wheels of a car rise when it takes a sharp left turn (that is it lurches towards the right)? Homework Equations $$a_c= V^2/R$$ The Attempt at a Solution I started by imagining the car as being a part of a very large ring, dx. Since it's taking a left turn...
  7. K

    Vectors symbol

    I see. Thanks a lot.
  8. K

    Vectors symbol

    I came across this while I was doing some questions on vectors.
  9. K

    Vectors symbol

    Î(o). o not 0.
  10. K

    Vectors symbol

    This problem is fairly objective (though quite stupid) What does î(o) represent? Does it refer to a vector making angle 0 degrees with the x axis? I searched but couldn't find the answer anywhere. Please help. Moderator note: post edited and moved from hoemwork
  11. K

    Kinematics chase problem

    Yes...that was what I wanted to know, because I had thought it would be a spiral but I didn't know the shape of it.Then I came across the logarithmic spiral, and it was the nearest shape that had come close to how I visualized the path. It was an intuitive guess, even though the parameters were...
  12. K

    Kinematics chase problem

    And is there another equation that can give me the desired information apart from this differential equation, or do I have to depend only on the problem statement for the same?
  13. K

    Kinematics chase problem

    The spiral I had mentioned was referring to a logarithmic spiral initially, before it attains a circular shape. More appropriately, it was a logarithmic spiral which terminated into a circle, because the radial component will keep on decreasing, and eventually it will become 0 otherwise in the...
  14. K

    Kinematics chase problem

    That was not what I meant. By path, I meant the trajectory it adopts before it has attained the desired radius. After that, I had taken it for granted that the particles move in concentric circles ( in my book, there was a hint given which said that). So, you mean that it can either keep on...
  15. K

    Kinematics chase problem

    So, it does follow the path of a spiral. What I wanted to know is how can you prove it mathematically. But I want to know what happens even if it is only transiently zero, and the mathematical aspect of it too.
  16. K

    Kinematics chase problem

    I believe it is the first one matching the trajectory of the circle( why is it SHM, though?), because eventually the particles probably move in concentric circles.
  17. K

    Kinematics chase problem

    The radial component of velocity is 0, or $$u=\omega r$$
  18. K

    Kinematics chase problem

    I'm sorry, I didn't get what you are saying.
  19. K

    Kinematics chase problem

    How did you formulate the equation for the path?
  20. K

    Kinematics chase problem

    As I mentioned earlier, please confirm whether the path will be a logarithmic spiral or any other shape.
  21. K

    Kinematics chase problem

    Sorry, I made an error. $$u^2=(\omega r)^2+v_r^2$$ So now I got a differential equation of the form $$\frac{dr}{dt}= (u^2-(\omega r)^2)^(\frac{1}{2})$$ And I'll solve it, with limits of R from 0 to ##R_u## with ##w=\frac{u}{R_u}## Thanks a lot. Also, for the problem of when it catches Q, maybe I...
  22. K

    Kinematics chase problem

    As I said, by equating the angular velocities, I got the radius $$R_u=\frac{u}{v}R_v$$ And for equating the radial component with ## \frac {dr} {dt}##, do we have r here as ##2\pi R## or simply as ##R## For your second observation ##u^2=\omega^2+v_r^2## Do I use the above equation in the...
  23. K

    Kinematics chase problem

    What I mean to say is P will move along a new circle with different components of angular and radial velocity having resultant u every instant. At that instant when it's radial velocity becomes 0, it will move in a circle
  24. K

    Kinematics chase problem

    Homework Statement Starting from the center of a circular path of radius R, a particle P chases another particle Q that is moving with a uniform speed v on the circular path. The chaser P moves with a constant speed u and always remains collinear with the centre and location of the chased Q...
  25. K

    Boy scout problem (Serway and Jewett)

    Yeah @above is right. I didn't explicitly mention what the variables were referring to. Here by x, I didn't mean the horizontal displacement in the equation, but the general form by which such an equation is represented. What I meant was $$\frac{dh}{dt}\frac{dv}{dh}=a$$ But as the above...
  26. K

    Boy scout problem (Serway and Jewett)

    It isn't x, is it? That's the only other variable distance on which velocity depends. On the other hand, do we have to integrate velocity w.r.t. Time to get that distance? To me the second one seems more appropriate, but then how to we find time? Which one to do, and why?
  27. K

    Momentum and energy conservation in a vertical loop

    If you've ever played loop the loop, in the game, we have to give a ball some velocity (kinetic energy) initially so that it can complete the loop. It's the same principle here. Say, your friend challenges you to make it to the top of the loop. You don't need to do the full loop, just reach the...
  28. K

    Boy scout problem (Serway and Jewett)

    h, since the velocity and acceleration are both in the direction of the vertical distance h
  29. K

    Boy scout problem (Serway and Jewett)

    Homework Statement To protect his food from hungry bears, a boy scout raises his food pack with a rope that is thrown over a tree limb at height $$h$$ above his hands. He walks away from the vertical rope with constant velocity $$v_b$$, holding the free end of the rope in his hands (a) Show...
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