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)##...
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...
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...
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...
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...
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...
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
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...
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...
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...
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...
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...
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...
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?
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...
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...
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...
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...
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...
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...
1. Homework Statement
Find the divergence of the function ##\vec{v} = (rcos\theta)\hat{r}+(rsin\theta)\hat{\theta}+(rsin\theta cos\phi)\hat{\phi}##
2. Homework Equations
##\nabla\cdot\vec{v}=\frac{1}{r^2}\frac{\partial}{\partial r}(r^2v_r)+\frac{1}{r sin\theta}\frac{\partial}{\partial...
1. Homework Statement
question :
find the value of
\iint_D \frac{x}{(x^2 + y^2)}dxdy
domain : 0≤x≤1,x2≤y≤x
2. Homework Equations
3. The Attempt at a Solution
so here, i tried to draw it first and i got that the domain is region in first quadrant bounded by y=x2 and y=x
and i...
How do i get an idea, or a 'feel' of the components of the acceleration in polar coordinates which constitute the component in the eθ direction?
from what i know, a= (r¨−rθ˙^2) er + (rθ¨+ 2r˙θ˙) eθ ;
(where er and eθ are unit vectors in the radial direction and the direction of increase of the...
General question, how do you determine the limits of integration of a polar curve? Always found this somewhat confusing and can't seem to find a decent explanation on the internet.
I am learning about the polar coordinate system, and I have a few conceptual questions.
I understand that in Cartesian coordinates there is exactly one set of coordinates for any given point. However, in polar coordinates there is an infinite number of coordinates for a given point. I see how...
1. Homework Statement
The functions are given:
##r(t)=pe^{kt}##
##\theta (t)=kt##
##v(r)=\sqrt2kr##
##a(t)=2k^2r##
Find the radius of the curvature of the trajectory in the function of ##r##
2. Homework Equations
$$R=\frac{(\dot x^2 + \dot y^2)^{3/2}}{(\dot x\ddot y - \ddot x\dot y)}$$
There...
1. Homework Statement
On the surface of a river at ##t=0## there is a boat 1 (point ##F_0##) at a distance ##r_0## from the point ##O## (the coordinate beginning) which is on the right side of the coast (picture uploaded below). A line ##OF_0## makes an angle ##θ_0=10°## with the ##x-axis##...