Particle moving with radial velocity

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Homework Help Overview

The problem involves a particle moving in a plane with a constant radial velocity and a constant angular velocity. The task is to determine the magnitude of the velocity and acceleration when the particle is at a specific distance from the origin.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between radial and tangential components of velocity, with one suggesting vector addition to find the final velocity. Others mention using polar coordinates for a more general approach to calculate speed and acceleration.

Discussion Status

There are various approaches being explored, including vector addition and polar coordinate equations. Some participants are seeking clarification on specific calculations, while others are suggesting alternative methods without reaching a consensus.

Contextual Notes

Participants are working within the constraints of the problem statement, which specifies constant radial and angular velocities. There is a mention of a potential formula for acceleration that raises questions about its applicability in this context.

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Homework Statement


A particle moves in a plane with constant radial r=4m/s. The angular velocity is constant and has magnitude [itex]\Theta[/itex]=2rad/s. When the particle is 3m from the origin, find the magnitude of the velocity and the acceleration.


Homework Equations





The Attempt at a Solution


The answer is v=root of 52 m/s. But I don't know how to get this number. Can somebody give me a hint?
 
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Radial velocity is constant at 4m/s.So when its 3m from origin,the tangential component of velocity is given by v=omega X r, ie 6m/s in this case
Now you have the mutually perpendicular radial and tangential components as 4m/s and 6m/s,calculate the final velocity by vector addition.
 
As an alternative to calculate speed and acceleration in Cartesian coordinates you may also want to find inspiration in the normal polar equations for velocity and acceleration, see for instance [1]. These equations are more general as they also allow for radial and angular accelerations, but in your case those are zero and inserting that you end up with two simple vector equations to take magnitude of.

[1] http://en.wikipedia.org/wiki/Polar_coordinate_system#Vector_calculus
 
Can I find acceleration by a=v[itex]\Theta[/itex]/(1-cos[itex]\Theta[/itex]t)?
 
Can somebody answer me?
 

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