Curvilinear Motion: Polar Coordinates (Engineering Dynamics)

In summary, the conversation discusses finding the equations for the r and θ components of acceleration in polar coordinates. The given equation for acceleration is a = (Rdouble dot - Rθdot2)eR + (Rθdouble dot + 2Rdotθdot)eθ, where the dot represents the derivative with respect to time. The goal is to manipulate this equation to be in terms of t or to solve for θ in terms of t and substitute it into the original equation. The final question asks for the equations for dr/dt and d2r/dt2 in terms of θ, dθ/dt, and d2θ/dt2.
  • #1
Andy907
2
0

Homework Statement



WtHMXSA.png


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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  • #2
In polar coordinates, what are the equations for the r and θ components of acceleration?
 
  • #3
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.
 
  • #4
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.
 

1. What is curvilinear motion?

Curvilinear motion is the motion of an object along a curved path. This type of motion can be described using polar coordinates, which involve the use of an angle and a distance from the origin.

2. How are polar coordinates used in engineering dynamics?

In engineering dynamics, polar coordinates are used to describe the motion of objects that move in a circular or curved path. This is particularly useful in situations where the motion is not along a straight line, such as in the case of rotating machinery or projectiles.

3. What is the difference between polar coordinates and Cartesian coordinates?

The main difference between polar coordinates and Cartesian coordinates is the way in which they describe the position of a point in space. While Cartesian coordinates use a horizontal and vertical axis to describe the position, polar coordinates use an angle and a distance from the origin.

4. How is velocity calculated in polar coordinates?

In polar coordinates, velocity is calculated by taking the derivative of the position vector with respect to time. This involves taking the derivative of both the angle and the distance from the origin.

5. What are some real-world applications of curvilinear motion in engineering dynamics?

Curvilinear motion and polar coordinates are used in a wide range of engineering applications, including the design and analysis of machinery, robotics, and aerospace systems. These concepts are also important in understanding the motion of planets and other celestial bodies in space.

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