How Do You Calculate the Acceleration of a Particle in Polar Coordinates?

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SUMMARY

The discussion focuses on calculating the acceleration of a particle moving in polar coordinates with constant radial velocity (r dot) of 4.3 m/s and constant angular velocity (theta dot) of 2.5 rad/s, at a distance of 3.1 m from the origin. The speed of the particle is determined to be 8.86 m/s using the equation v = √((r dot)² + (r * theta dot)²). To find the magnitude of the acceleration, participants are advised to take the derivative of the velocity equation with respect to time, considering that r dot is constant.

PREREQUISITES
  • Understanding of polar coordinates and motion in a plane
  • Familiarity with calculus, specifically differentiation
  • Knowledge of kinematic equations for velocity and acceleration
  • Basic understanding of angular velocity and radial velocity concepts
NEXT STEPS
  • Learn how to differentiate functions involving square roots in calculus
  • Study the relationship between angular velocity and linear velocity in polar coordinates
  • Explore the concept of centripetal acceleration in circular motion
  • Practice problems involving acceleration in polar coordinates using different values for r dot and theta dot
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion in polar coordinates, as well as educators seeking to enhance their teaching of these concepts.

toastie
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Homework Statement


A particle moves in a plane with constant radial velocity (r dot) and constant angular velocity (theta dot). When the particle is at distance r from the origin, determine the magnitude of the acceleration.

r dot = 4.3 m/s
theta dot = 2.5 rad/s
r = 3.1 m
speed of the particle at r = 8.86 m/s


Homework Equations


v = (((r dot)^2)+((r*(theta dot))^2))^.5


The Attempt at a Solution


I have attempted to find the derivative of the above equation, but I am not sure if I am doing the derivate wrong.
 
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toastie said:

Homework Statement


A particle moves in a plane with constant radial velocity (r dot) and constant angular velocity (theta dot). When the particle is at distance r from the origin, determine the magnitude of the acceleration.

r dot = 4.3 m/s
theta dot = 2.5 rad/s
r = 3.1 m
speed of the particle at r = 8.86 m/s

Homework Equations


v = (((r dot)^2)+((r*(theta dot))^2))^.5
You have the right expression for the magnitude of v as a function of r. Take the derivative with respect to time. Since [itex]\dot r[/itex] is constant with time, what is its derivative?

[tex]|a| = |dv/dt| = \frac{d}{dt}\sqrt{|\dot r|^2 + \omega^2r^2}[/tex]

AM
 
thanks for the help
 

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