Radius Definition and 1000 Threads

The radius of a circle is r units. By how many units should the radius be increased so that the area increases by b units? The information in this problem tells me that using the area of a circle formula is needed. A = pi•r^2 I think b should be added to r and squared. A = pi(r + b)^2 Can...

Hello everyone! This is my first post here so please excuse me if I don't have the format right yet. Background: I'm a Mechanical Engineering student working on a robotics team and I'm tasked with designing the wheels. The robot is currently using 5 in radius wheels with old motors. The...

Homework Statement Two fully equal sphere's of lead are placed next to each other so that the gravitational force between sums up to 10N. Calculate mass and radius of the two sphere's. F=10N , ρlead=11300kg/m2 Homework Equations F=gm, F=GMm/r2 , V=4πr3/3 , ρ=m/VThe Attempt at a...

{Moderator note: Member advised to retain and use the formatting template when starting a thread in the homework sections} Hey guys Question: Calculate the divergence as a function of radius for each of the following radially symmetrical fields in which the magnitude of the field vector: (a)...

A 2.53*10^(-6) C charged particle with kinetic energy of 0.0929 J is fired into a uniform magnetic field of magnitude 0.147 T. If the particle moves in a circular path of radius 3.38 m, determine its mass in kg. (answer should be within 2*10^-14 kg) The formula r=mv/qb comes to mind where r is...

Homework Statement [/B] Find the radius and center of sphere ρ = 28 cos ϕ. Homework Equations Relevant equations would be the spherical and rectangular coordinate equations. The Attempt at a Solution I started off by multiplying both sides of the equation by ρ to get ρ^2 = 28 ρ cosϕ Then...

How is this done? My textbook only specifies integrating polar graphs with respect to theta.

Homework Statement [/B] A wheel, of radius 200mm, rolls over the top of a hill with a speed of 20m/s and negligible friction losses. (I = 1/2mr^2) Homework Equations [/B] Find the speed of the wheel when it is 10m below the top. The Attempt at a Solution [/B] mgh = 1/2mv^2 + 1/2IW^2 W=...

The area of a circle as a function of its radius. The textbook answer is A(r) = πr^2. I cannot make the connection between the words and the equation. What does A(r) mean? I know that πr^2 means "pi times (radius) squared" but what does it really mean? Why is the radius squared in the...

Homework Statement A particle moves along a circular path over a horizontal xy plane at a constant speed. At time t1= 3.00s, its acceleration vector is given by (3i-5j) m/s^2. At time t2=7.00 s, its acceleration is given by (-3i+5j) m/s^2. Find the radius of the particle's circular path...

Hey guys, The following thing got me a little bit messed up. I want to calculate the orbital radii of an Hydrogen atom if the angular velocity of the electron is 10^16 * s^-1. At first i set the centripetal force and the electrostatic force as equals. ( m * v^2 )/ r =k * (e^2) /...

1. Sketch the circle of radius 1 centered at (0, 0). (A) Write the equation of this circle. I must use x^2 + y^2 = r^2. The radius is 1. This means r = 1. The equation is x^2 + y^2 = 1. Correct? B. Does the point (3/5, 4/5) lie on this circle? (3/5)^2 + (4/5)^2 = 1^2 (9/25) + (16/25) = 1...

Homework Statement Homework Equations Centre of gravity: X=m1x1-m2x2/m1-m2 MOI rectangle: 1/3ml^2 MOI triangle: 1/18md^2 Radius of gyration: Ixx=mk^2 The Attempt at a Solution Mass of body 1: b*l*p = 0.8*1*10=8kg Mass of body 2: 1/2b*h*p = 1/2(0.4)*0.6*10=1.2kg1.1 X=m1x1-m2x2/m1-m2...

Homework Statement Consider the Earth's orbit around the sun orbit as circular. Suppose the sun slowly loses mass from mass M1 to mass M2. Suppose that the initial orbit is R1 and the final orbit is R2. Express R2 in terms of the other parameters. 2. The attempt at a solution The problem I'm...

Homework Statement A mass ##m## whirls around on a string which passes through a ring. Given that gravity is not present and initially the mass is at a distance ##r_0## from the center and is revolving at angular velocity ##\omega_0##. The string is pulled with constant velocity ##V## starting...

Find the moments of inertia about the x-axis, y-axis and the origin. Also, find the radius of gyration about the x-axis and y-axis. y = 0, y = b, x = 0, x = a Rho = ky 1. Is ky the density function? 2. Do I integrate over dxdy or dydx? 3. Are the limits of integration y = 0, y = b, x = 0...

Homework Statement If the centripetal force is at the left side of the equation; that means if we move it over to the other side, it'll have a negative sign, which means it is opposite in sense in relation to N and mg. But how is that possible, considering that the centripetal force always...

Homework Statement Let g be the acceleration due to gravity at the Earth's surface and K be the rotational kinetic energy of the Earth. Suppose the Earth's radius decreases by 2%. Keeping all other quantities constant, (a) g increases by 2% and K increases by 2% (b) g increases by 4% and K...

In simple terms, what exactly is the radius of gyration as taught in Calculus 3? Is gyration connection in any way to rotation?

Homework Statement Using the viscosity of air as 1.8x10-5Pa s, and the density of water as 1x103kg m-3, find the radius of a raindrop traveling at a terminal velocity of 7.05ms-1. Assume Stokes law can be used. The problem is finding the density of air, I could use F = 6rvπη but I don't know...

Hello, I am curious to see how the mathematical analysis of a vertical circular motion with a sensible rope, that is to say, a rope that streches easily, looks like. k- constant of the rope. thanks,

This being WRT resonating pipes. Apparently the acoustical length of the pipe is different to the physical length due to the vibration of the sound particles moving the particles at the opening so that the physical length is no longer the length of resonance. I've found many sources on the...

Hello, I did a calculation to determine whether a liquid with a fixed volume ##V##, would be spread over a larger surface area ##A## on the inside mantle of a cylinder, if the cylinder has a larger radius ##r##. So I’d like to find a relationship between the radius ##r## and the area ##A## over...

Homework Statement A single ionized uranium ion of mass 6.9 x 10 ^-25 kg is accelerated through a potential difference of 4.4 x 10^5 V. What is the radius of the path it would take if injected at 90 degrees into 0.47 T uniform magnetic field at this velocity? 3. Attempts Since centripetal...

Homework Statement a golfer hits a golf ball so that it has an initial velocity of 165mph and 12 degrees above the horizon. I already know the radius of curvature when the ball is hit. but my question is, will the radius be that same when it hits the ground? Homework Equations an=v2/ρ The...

Homework Statement The athelete releases the shot with velocity v = 16 m/s at 20° above the horizontal. What is the instantaneous radius of curvature of the shot’s path when it is at the highest point of its trajectory? Enter an answer in meters up to the first decimal place. Use g = 9.81...

(mentor note: posted in a non-homework forum hence no template) Hello! I have a problem I'm trying to solve. I'm transforming a circle with known radius. Knowing it's radius i can calculate the circumference. I transform it by squeezing one side, leveling it, creating a circle segment with a...

Homework Statement Calculate the radius of a 1.3 Msun white dwarf using the mass-radius relation for white dwarfs. Give the answer in solar radius. Homework Equations Mass-radius relation: $$R \propto M^{-\frac{1}{3}}$$ The Attempt at a Solution So I've tried the following: $$R_{D} \propto...

Determine the center and the radius of circle. x^2 + y^2 - 10x + 2y + 17 = 0 Can this be done using completing the square?

The radius of a circle is r units. By how many units should the radius be increased so that the area increases by b square units? I don't know where to begin. A = πr^2 Does this question involve the area of a circle formula? If so, in what way?

Homework Statement A single-turn wire loop produces a magnetic field of 41.2 μT at its center, and 5.15 nT on its axis, at 20.0 cm from the loop center. Find loop raidus and current. Homework Equations F = qv x BThe Attempt at a Solution I tried to use the above equation, but could not figure...

$\tiny{10.7.37}$ $\displaystyle\sum_{n=1}^{\infty} \frac{6\cdot 12 \cdot 18 \cdots 6n}{n!} x^n$ find the radius of convergence I put 6 but that wasn't the answer

Homework Statement A pulley of radius, R and moment of inertia, I=2MR^2 is mounted on an axle with negligible friction. Block A, with a mass M, and Block B, with a mass of 3M, are attached to a light string that passes over the pulley. Assuming that the string doesn't slip on the pulley, Answer...

Hello, everyone! Now I'm trying to develop 2 wheels robot, which travels along the line simulator. The robot can turn only by increasing velocities of each wheel. The conditions are below: - I know velocities of 2 wheels - I know radius between wheels The task is next: How to find new location...

I was not sure if this was the best place for this, it could fit here, in the Chemisty section or the Programming section. So feel free to move if needed. Essentially I have been modeling polymers in python and using a Monte Carlo, Metropolis type algorithm, to minimise its energy into...

Homework Statement A particle of mass m is moving on a frictionless horizontal table and is attached to a massless string that passes through a tiny hole of negligible radius in the table, and I am holding the other end of the string underneath the table. Initially the particle is moving in a...

Homework Statement An disk has a radius of 0.2 meters. A lump of putty with a coefficient of static friction of 0.9 is stuck on the edge of the disk. Let's say the disk starts at rest and gradually speeds up. At what speed will the putty just barely be able to stay in place on the edge of the...

I have a question for my Astro homework and I am a little unsure as to whether I am going in the right direction Question Using an expression that relates luminosity, size and temperature of a star, and assuming all Main Sequence stars have the same mean density, determine the relationship...

While going through the derivation to find the surface tension of liquid i came with the formula which says that the surface tension is directly proportional to radius of the capillary so does that imply if we use a capillary with a greater radius so the same will give the different value of...

Hello, I’ve been watching a lecture about how in astronomy one would be able to calculate the radius of 2 stars by measuring the velocity of the orbit and then measure the time how long the luminosity of a star dims when one star is behind the other. After thinking this a bit through, I came...

I want to find how far a gear from a rack and pinion will rotate from the displacement of the rack and the angle that it will have turned using: s=r*angular displacement. So what is the radius in this case?

Correct if I'm wrong. V(esc.)=(2GM/R)^1/2 that is equal to R=2GM/V^2 putting v=c,we get R=2GM/c^2 by putting the value of G,M,C we get schwarzschild radius=1.46*10^-27 m/kg

Homework Statement My textbook states that, "Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force". But my question is, why, and how is that true? I would have assumed at first that if the radius was getting shorter, then the centripetal force...

Hello everyone, I am working on a project in astrophysics in which I need to include now some type of particle distribution (as a function of the radius). I was wondering if there is some accepted function that would describe the number of particles per radius in astrophysics. Saturn's rings...

Hi, I was thinking of the slip that is defined as following: $$ s = \frac{R\omega}{v_x} -1 $$ The definition of the effective radius according to Chand and Sandu [1] $$ \begin{equation} R_e = \left\{ \begin{array}{l l} R - R \left(1- \frac{1...

So if I drop an apple, we can consider the ground accelerating upwards and the apple still. And the radius of the Earth doesn't change due to space time being curved. I'm having a hard time conceptualizing this. Is it analogous to a classically orbiting object? Classically, under simplfying...

Question :- The critical volume of a gas is 0.072 L mol-1. What will be the radius of the molecule in cm ? Answer in the book :- ##V_c = 3b \implies b = 0.024 L mol## ##\therefore## for every molecule ##b = {24 \text{cm}^3\over 6 \times 10^{23}} = 4 \times 10^{-23}\text{cm}^3## per...

What is the exciton Bohr radius? I understand that the exciton is the paired distance of an electron and hole. How does the Bohr radius play a role in this?

Homework Statement Homework Equations Ratio test. The Attempt at a Solution [/B] I guess I'm now uncertain how to check my interval of convergence (whether the interval contains -2 and 2)...I've been having troubles with this in all of the problems given to me. Do I substitute -2 back...

Homework Statement Hi everybody. I am currently trinyg to solve the first exercice of the fifth chapter of R.R. Rogers book about cloud physics. "Show that the vapor pressure in equilibrium over a pure water drop of radius r decreases with T if r<2σ/LρL. Homework Equations...