polar coordinates

1. I Converting Velocity Vector Formula from Cartesian Coordinate System to Polar Coordinate System

I have a little question about converting Velocity formula that is derived as, $\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}$ in Cartesian Coordinate Systems $(x, y, z)$. I want to convert this into Polar Coordinate System $(r, \theta)$...
2. How to get $\ddot r$ when you have $r$, $\theta$ and right trig

I have a right triangle: one of the angles is $60°$ (that's $\theta$), one of the sides is $40 m$ long, and the hypotenuse is equal to the radius. Now I can find an expression for $r$ and that expression is $r=\frac{height}{sin \theta}$. If I differentiate it, I'll get $\dot r$ and...
3. Calculating the radius of curvature given acceleration and velocity

Well, what I've done so far is calculating the magnitude of velocity and acceleration replacing $t=2$ in $\theta (t)$ and $r(t)$ so I could get the expressions for $\dot r$, $\dot \theta$, $\ddot r$ and $\ddot \theta$. But that's not my problem... my problem is related to the...
4. Angular and orbital speed at perihelion

Hello to all good people of physics forums. I just wanted to ask, whether the angular and linear (orbital) speed in perihelion of eliptical orbit are related the same way as in circular orbit (v = rw). If we take a look at the angular momentum (in polar coordinates) of reduced body moving in...
5. Convert cylindrical coordinate displacement to Cartesian

Summary: I can't figure out how the solver carries out the conversions from cartesian to cylindrical coordinates and vice-versa. I have a set of points of a finite element mesh which when inputted into a solver (ansys) gives the displacement of each node. I can get the displacement values of...

7. Finding the movement equation (non intertial system)

1. Homework Statement A particle of a mass $m$ is embedded in a circular rail, (radius: $R$), without any friction. In a given moment, the particle finds itselfs without velocity at point C, and a force is applied on the rail, which starts moving with an $\vec A$ constant acceleration...
8. I Difference Between Inward and Outward Spiral Curves

Could anyone please explain how can I know mathematically whether the logarithmic spiral curve spirals inward or outward? In which sense does the outward spiral spirals? Thank you very much for your help
9. Polar equation of a hyperbola with one focus at the origin

1. Homework Statement Hello everyone, I have an assignment (Spivak's Calculus) to show that the polar equation of a hyperbola with the right focus in the origin is $r=\frac {±\Lambda} {1+εcos(\theta)}$, but the equation I reached was slightly yet somewhat disturbingly different, and I'm not...
10. I Radial Acceleration in Polar/Cylindrical Coordinates

My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ? If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...
11. Finding area enclosed by the polar curve

1. Homework Statement Question attached in attachments 2. Homework Equations Area enclosed by polar graph is ∫0.5r^2 where r is the radius as a function of angle theta 3. The Attempt at a Solution I attempted to use the formula above and I subtracted the area of the inside from the outside...
12. Line passing through the origin (polar coordinates)

1. Homework Statement -infinity < r > +infinity Which of the following are equations for the line y=m*x for m<0: a. theta = -arctan(m) b. theta = arctan(m) c. theta = arctan(-m) d. theta = arctan(m) + pi e. theta = arctan(m) - pi f. r = 1/(sin(theta - arctan(m))) 2. The attempt at a...
13. Diffusion equation in polar coordinates

1. Homework Statement I am trying to solve the axisymmetric diffusion equation for vorticity by Fourier transformation. 2. Homework Equations $$\frac{\partial \omega}{\partial t} = \nu \Big( \frac{1}{r}\frac{\partial \omega}{\partial r} + \frac{\partial^2 \omega}{\partial r^2} \Big).$$ 3...
14. D

Finding the volume surrounded by a curve using polar coordinate

1. Homework Statement I tried to answer the following questions is about the curve surface z= f (x, y) = x^2 + y^2 in the xyz space. And the three questions related to each other A.) Find the tangent plane equation at the point (a, b, a^2+ b^2) in curved surface z . The equation of the...
15. A child slides down the helical water slide AB (Polar Coordinates)

1. Homework Statement 13.43 A child slides down the helical water slide AB. The description of motion in cylindrical coordinates is $R=4m$, $θ=ω^2t^2$ and $z=h[1-(\frac {ω^2t^2} {π})]$, where h=3m and ω=0.75rad/s. Compute the magnitudes of the velocity vector and acceleration vector when...
16. Cloverleaf highway interchange - determine car acceleration

1. Homework Statement 13.34 The curved portion of the cloverleaf highway interchange is defined by $R^2=b^2sin2θ$, 0<=θ<=90deg. If a car travels along the curve at the constant speed v0, determine its acceleration at A 2. Homework Equations 3. The Attempt at a Solution Is this wrong?
17. Determine the angular speed $\dotθ$ of the arm OC

1. Homework Statement 13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v0, determine the angular speed $\dot θ$ of the arm OC in terms of v0, b, and θ. 2. Homework...
18. The collar B slides along a guide rod (Polar Coord.)

1. Homework Statement 13.29 The colar B slides along a guide rod that has the shape of the spiral R = bθ. A pin on the collar slides in the slotted arm OC. If OC is rotating at the constant angular speed $\dot θ = ω$, determine the magnitude of the acceleration of the collar when it is a A...
19. The rod OB rotates counterclockwise about O (Polar Coord.)

1. Homework Statement 13.25 The rod OB rotates counterclockwise about O at the constant angular speed of 45 rev/min while the collar A slides toward B with the constant speed 0.6 m/s, measured relative to the rod. When collar A is in the position R = 0.24m, θ = 0, calculate (a) its velocity...
20. A particle travels along a plane curve (Polar coordinates)

1. Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...
21. I Q about finding area with double/volume with triple integral

So when finding the Area from a double integral; or Volume from a triple integral: If the curve/surface has a negative region: (for areas, under the x axis), (for volumes, below z = 0 where z is negative) What circumstances allow the negative regions to be taken into account as positive when...
22. Object moving on a spiral figure

1. Homework Statement We've got an object/person in the center of a cicrcle that spins around with an angular velocity ω. That same object is moving at a constant speed k with the direction of the radius, that is from the center to the outside of the sphere. That object describes then a spiral...

30. Having a hard time writing equations of motion...

1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution