Curvilinear Motion: Polar Coordinates (Engineering Dynamics)

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SUMMARY

The discussion focuses on curvilinear motion in polar coordinates, specifically addressing the equations for the radial (r) and angular (θ) components of acceleration. The acceleration vector is defined as a = (R'' - R(θ')²)eR + (R(θ'') + 2R'θ')eθ, where R represents the radial distance. The participant seeks guidance on expressing r in terms of time (t) and understanding the derivatives involved, particularly dr/dt and d²r/dt² in relation to θ and its derivatives.

PREREQUISITES
  • Understanding of polar coordinates in physics.
  • Familiarity with derivatives and their notation (e.g., R', R'').
  • Knowledge of acceleration components in curvilinear motion.
  • Basic principles of dynamics and kinematics.
NEXT STEPS
  • Study the derivation of the radial and angular components of acceleration in polar coordinates.
  • Learn how to manipulate equations involving R and θ to express them in terms of time.
  • Explore examples of curvilinear motion problems that involve polar coordinates.
  • Investigate the relationship between angular velocity and radial acceleration.
USEFUL FOR

Students and professionals in engineering dynamics, particularly those studying motion in polar coordinates and seeking to solve related problems in curvilinear motion.

Andy907
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Homework Statement



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Homework Equations

The Attempt at a Solution


I have stared at this for hours and don't know where to start. I think I need to get r in terms of t but I don't really know how with the information given. I just need a good hint to get started.
 
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In polar coordinates, what are the equations for the r and θ components of acceleration?
 
Chestermiller said:
In polar coordinates, what are the equations for the r and θ components of acceleration?

a = (Rdouble dot - Rθdot2)eR + (Rθdouble dot + 2Rdotθdot)eθ

I know a = 15 m/s2. I also know that the dot means the derivative is taken in respect to time. That's where I'm drawing a blank and why I thought the given R equation had to be manipulated in some way to be in terms of t. Or possibly solve for θ in terms of t and then substitute that equation into θ in the original given R equation.

In all the examples we did in class θ was given in terms of t, so it was pretty simple to substitute that equation into the given r equation and then take the derivatives.
 
From Eqn. 3.1, in terms of dθ/dt and θ, what is dr/dt?
What is ##\frac{d^2r}{dt^2}## in terms of θ, dθ/dt, and d2θ/dt2.
 

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