Circular Definition and 999 Threads

I know that in order for the two lights to be distinguishable from one another they have to be separated by an angle of at least theta = 1.22(wavelength)/(width of aperture). I tried drawing the given picture below and then using trig to find L in terms of d/2 and theta/2. However, this ended up...

I am attempting to calculate the Fresnel difraction pattern from different diameter circular apertures for specific source to aperture and aperture to sensor distances. I'm generally following the procedure given in Klaus D. Mielenz "Algorithms for Fresnel Diffraction at Rectabngual and Circular...

I have attempted to solve for the velocity by setting the centripetal force (mv2)/r to the normal force pointed to the center of rotation (mg). This approach seems to give the incorrect solution and I am unsure of my misunderstandings.

#F= m\frac{v^2}{r} = mw^{2}r# #m=5# #r=0.9# #F= 5\frac{v^2}{0.9} = (0.9)5w^{2}# #5\frac{v^2}{0.9} = (0.9)5w^{2}# #\frac{v^2}{0.9} = (0.9)w^{2}# #v=0.9w# then I get stuck cause I have both unknowns in one equations (i bet it has something to do with the question’s use of “minimum” but I...

Problem Statement : Solve for ##x## : Attempt : If I take ##x=\tan\theta##, the L.H.S. reads $$\tan^{-1}\frac{1-\tan\theta}{1+\tan\theta}= \tan^{-1}\left[\tan\left(\frac{\pi}{4}-\theta \right) \right ]=\frac{\pi}{4}-\theta.$$ On going back to ##x## from ##\theta##, the given equation now...

In the solution manual, it says that: the resultant of friction force is ##<= kmg##, hence $$m\sqrt{\omega_t^2 + (\frac {v^2} {R})^2} <= kmg$$ and from this equation, we will get $$v^2 <= R \sqrt{(kg)^2 -\omega_t^2}$$ which will make ##v_{max}^2= R \sqrt{(kg)^2 -\omega_t^2}## Finally, they...

For a Prandtl stress function to be valid, it must be zero on the boundary. For a circular bar, both of these work: $$\phi_1 = C\left(\frac{x^2}{r^2}+ \frac{y^2}{r^2} - 1\right)$$ $$\phi_2 = C \left(x^2+ y^2- r^2\right)$$ But performing the integration for the internal torque M gives...

Hello! This is a problem from Halliday Resnick Krane (Chapter 4: Problem #15). “A puck is moving in a circle of radius r0 with a constant speed v0 on a level frictionless table. A string is attached to the puck, which holds it in the circle; the string passes through a frictionless hole and is...

Suppose we have a vertical circular motion with gravity according to the image below. In the leftmost and rightmost positions the resultant force is pointing diagonally down. Isn't the resultant force supposed to be pointing at the center at all times in a circular motion? What am I getting...

This is my solution ,and I just use the definition .But I still feel unclear about the concept of non-conservative force.$$ W = F x = 30N (\frac{1}{2}\pi r ) = 56.2 J $$ $$ E_{system} = \Delta K + \Delta U = W $$ $$ (K_{f}- K(i))+(U(f)-U(i)) = W $$ $$ (\frac{1}{2} *m{V_{f}}^2...

The strategy will be to figure out what ##dq##, ##\hat{r}_{dq,p}##, and ##r_{dq,p}## are, plug them into the expression for ##d\vec{E}_{p_r}##, then integrate over ##d\vec{E}_{p_r}## to obtain ##\vec{E}_{p_r}##, the electric field at ##P## due to the arc on the right. Then I will repeat the...

My question is, is this correct, and if so, why the minus sign?

This is an offshoot of @Angela G 's thread. I don't want to hijack her thread so I decided to create a new one. Original thread https://www.physicsforums.com/threads/unstable-or-stable-electrostatic-equilibrium.1007881/ @kuruman @PeroK @bob012345 If you have the time I'd appreciate your input...

Hi :) This is a problem from David Tong's Classical Dynamics course, found here: http://www.damtp.cam.ac.uk/user/tong/dynamics.html. In particular it is problem 6ii in the first problem sheet. Firstly we can see the lagrangian is ##L = \frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2) -...

Consider that the particle is moving in circular with tangential velocity v, and (0,0)is its origin. I wonder why dr/dt is equal to tangential velocity instead of radial velocity (since dr/dt means how much change in radial distance in a really short duration of time)

In a previous thread* the field in a charged ring was discussed and it was shown to be not zero except at the center. In *post #45 a video is referenced that says the field diverges as one gets close to the ring and it was argued that at very close distances the field looks like an infinite line...

(I drew motion in the opposite direction so the object would rotate trigonometrically but it should be the same thing) I have just finished the Kinetic Energy and Work chapter in my course and this is the last problem from the problem set. I have not worked many problems with the Work-Kinetic...

I have broken the ring into a top arc and a bottom arc. First, let's assume an imaginary charge of +1 C is placed at point P. We will determine the force on this unit charge from top and bottom arcs. The charges in the top arc will result in electric fields that will all cancel each other...

I can evaluate the first beads motion easily A to B is -2Rj considering the point B as y=0 the motion of the bead will be -gt^2/2+2R=0 which implies t=2√(R/G) , this is ok but what I am struggling with is A to C I can see that the angle between the beads weight and it's negative normal force...

(I must confess that, in spite of working through the chapter on inverse circular functions, I could barely proceed with this problem. Note what it asks to prove : ##x\sqrt{1-x^2}+\ldots## and how much is that at odds with the formula (1 above) of adding two ##sin^{-1}##'s, where you have...

I couldn't fit in the title, but this is with a hollow circular cross section So currently I am trying to figure what occurs when two, perpendicular bending moments are applied to a hollow circular cross section (one about the z axis, and the other about y). I know that if I was dealing with a...

Is it possible for the stone to move in horizontal circular motion just like in the picture? I try to draw the free body diagram of the stone and there are two forces acting on the stone, its weight (directed downwards) and the tension of the string (directed to the left). The tension will...

I would really appreciate some help with this problem regarding non-uniform circular motion, in which a body is accelerating as it follows a circular path. If we take Example 1, a body starts at Point A with an angular speed of 180°/s. The body accelerates to Point B and reaches it some time...

At t= 0, we can see that the particle P has a radial acceleration of ##-2\hat j## and a tangential acceleration of ##2 \hat i##. The radial acceleration will tend to move it in a circle of a certain radius, whereas the tangential acceleration will tend to displace it parallel to x- axis...

Can a point P on the smaller wheel trace a straight line path inside the circular road (like the walls of a well)

Hello, Apologies if this is in the wrong section, it's related to circles so I figured Geometry was the best place. I found a very good example online that explains how to determine a future position of an object undergoing uniform circular motion: (Note that they made a mistake by writing...

I'm trying to solve this problem using an rtz coordinate system, and Newtons second law. I know that mar = (m(v)2)/r. I'm failing to understand how mg and the drag force affects the solution and how I would set it up. I know if it was at the bottom of the circle that mg would be added to the...

Looking at the wikipedia page for the (original) quantum eraser (https://en.wikipedia.org/wiki/Quantum_eraser_experiment), quarter-wave plates in front of the slits change photons from being linearly polarized to being circularly polarized. I think this is the case when there is no polarizer in...

First I figured out the normal force being exerted on the car using the equation above. Cos(40°)*(1050*9.8) = 7883N Next, I tried to find out the horizontal component of the normal force by doing: Cos(50) * 7883 = 5067N I figured out the angle by using certain geometrical properties. Next, I...

I was pondering my practice of talking about circular motion in the horizontal direction and the vertical direction. But I'd often would see in books, notes, and the internet that we assume constant velocity for the vertical case. However, when one thinks about the forces at different points in...

Question 1: I believe that the ratio would be b. 8:1 because by combining the formula for kinetic energy and momentum the expression Ek=p^2/2m can be obtained. Thus, for a body of mass 2kg with twice the momentum: Ek=2^2/2*2=1 For a body of mass 4kg with half the momentum: Ek=1^2/2*4=1/8...

Suppose a particle is moving around a circular track of radius R at speed v. To bend around a circle some agency has to exert an acceleration towards the center of the circle. I analyze the forces acting on the particle, its weight and the normal force and there is no acceleration in the...

a)Determine the slowest speed that the keys can swing and still maintain a circular path. Fnet = Fg + Ft Fc = Fg + Ft When Ft = 0, Fc = Fg So, Fc = mv^2 / r and Fg = mg mv^2/r = mg v = √gr v = √9.81 * 0.25 v = 1.56 m/s Therefore, the slowest speed that the keys can swing and still maintain...

If you take a horseshoe magnet and fuse the north and South Poles together (without destroying the magnetic field) would you have a “pole-less” magnet? And if so, what special properties would it have(other than other magnets)?

Help please

The only thing I can think of is that to create a circularly polarized wave the axes of the quarter wave plate will have to be at 45 degrees to the E vector. Only then it can have both components on the slow and fast axis equal. Then the slow axis will cause delay and the resulting vector will...

I think that the intensity of output of circularly polarised light falling on an analyser should not depend upon the axis of analyser. Because it is circularly polarized. It keeps rotating. So, the output should be linearly polarised. The amplitude of E field in the direction of analyser is a...

Please I do not want the answer, I just want understanding as to why my logic is faulty. Included as an attachment is how I picture the problem. My logic: Take the volume of the cone, subtract it by the volume of the cylinder. Take the derivative. from here I can find the point that the cone...

I have understood everything till 2nd paragraph. But after that everything was above my head. Can you explain me the concept

At page 20 of this pdf the two formulas that characterize the behavior of a linear and a circular antenna array are compared. The reason why I write this post is: I don't understand why the second formula is true. Below I show why I am not convinced. In general, given a configuration of sources...

N.B. I have inserted the proof here as reference. See the bolded text. My question is, isn't the reasoning "##x^{2}+5 \varepsilon<2,## thus ##(x+\varepsilon)^{2}<2 .## " circular? If we can already find an ##0<\varepsilon<1## such that ##x^{2}+5 \varepsilon<2,## Can't one also claim that " we...

does an em wave with circular polarization behave like a coil, i.e. do perpendicular electromagnetic fields join internally? I am very confused on this subject

Not sure what I'm doing here. Not sure how to continue? Please help. Thank you in advance!

Basically, I need help to continue on this question. This is what I have now: Angle of the race track (angle of the grey part): tan(18/(169-108)) = 0.30396 Not sure how to continue?? What am I supposed to do and find next? Thank you in advance! :smile::blushing::oldbiggrin:

The Lorentz's force acting on a charged particle perpendicularly "hitting" a magnetic field will be directed upwards, and generally directed towards the center of the circumference traveled by this particle, and so will cause a centripetal acceleration to keep it in a circular motion. By...

Does circular freefall of an object involve cancellation of gravitational and inertial forces, as it does in linear freefall?

This is actually right at the start of another derivation, but I can't understand how the author gets the formula for ##q##. So the discharge per unit thickness is the circumference of the circle, multiplied by the velocity at that point (at ##r##)? I thought the formula for flow rate was...

Summary:: I have recently started with data structures in java and I tried doing this Program .But I have few confusions. 1.How do I write the main() of the program? 2.What are we supposed to do with the value returned by function pop()? If anyone could point out if there are any errors and...

I learned about Bessel functions and steady-state temperature distributions in the past. Recently, I was searching online for some example problems on the topic and found the "original question" along with the solution online as a PDF file. While I am unsure will it be appropriate for me to...