Dynamics, polar coordinate system

In summary, the question asked for the magnitude of acceleration given the values of theta, r, dr/dt, and d^2r/dt^2. The process involved calculating the angular velocity and acceleration with the given conditions and then using them to find the resultant acceleration using the polar coordinate system formula. However, the calculated value of 357.7 ms^-2 was deemed incorrect by the dynamics lecturer due to incorrect numbers used in the calculation. The correct values for radial and theta accelerations are -282.912 ms^-2 and 218.88 ms^-2 respectively.
  • #1
bartieshaw
50
0
i have been set the following question

theta = 3r^2
find the magnitude of the acceleration when

r=0.8 m
dr/dt = 4ms^-1
d^2r/dt^2 = 12 ms^-2

my working followed the process of calculating angular velocity with these conditions and angular acceleration with these conditions then plugging them into the acceleration formula for a polar coordinate system.

when doing this i get

a(radial) = -282.912 ms^-2 (componant along the radius)
a(theta) = 218.88 ms^-2 (componant perpendicular to radius)

using pythagoras to calculate the magnitude of the resultant acceleration i get a value 357.7 ms^-2

a value my dynamics lecturer is prompt to tell me is WRONG. perhaps someone can help me...PLEASE
 
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  • #2
Your numbers are wrong. I don't see how you could get them.
The radial acceleration is GIVEN to you as 12 m/s^2.
You have to relate d^2theta/dt^2 to d2r/dt^2 by differentiating the equation
theta=3r^2 twice. Then rd^2theta/dt^2 s gives a(theta).
 
  • #3



Thank you for sharing your working and results. It seems like you have followed the correct process for finding the magnitude of acceleration in a polar coordinate system. However, it is possible that there might be a mistake in your calculations. I would suggest double-checking your calculations and making sure that you have accounted for all the units correctly.

Additionally, it might be helpful to review the formula for acceleration in a polar coordinate system, which is given by:

a = (d^2r/dt^2 - r(dtheta/dt)^2)er + (2(dr/dt)(dtheta/dt) + r(d^2theta/dt^2))e(theta)

Where er and e(theta) are unit vectors in the radial and tangential directions, respectively.

Also, make sure that you are using the correct values for r, dr/dt, and d^2r/dt^2 in your calculations. Sometimes, small errors in input values can lead to significant differences in the final result.

I would also recommend consulting with your dynamics lecturer or a tutor for further clarification and guidance. They might be able to spot any mistakes in your calculations and help you understand the correct approach for solving this question.

I hope this helps. Best of luck with your studies!
 

What is dynamics in the polar coordinate system?

Dynamics in the polar coordinate system refers to the study of the motion and forces acting on objects in a two-dimensional space using polar coordinates. It involves analyzing the position, velocity, and acceleration of objects in terms of their radial distance and angular direction.

What are the advantages of using polar coordinates in dynamics?

Polar coordinates offer several advantages in dynamics, including simplifying the mathematical equations and providing a more intuitive understanding of circular and rotational motion. They also allow for easier visualization of complex trajectories and make it easier to analyze forces acting on objects in curved paths.

How are forces represented in the polar coordinate system?

In the polar coordinate system, forces are typically represented in terms of their radial and tangential components. The radial component is the force acting towards or away from the center of rotation, while the tangential component is the force acting perpendicular to the radial direction, causing rotation.

What is the relationship between polar and Cartesian coordinates in dynamics?

Polar and Cartesian coordinates are two different systems for representing points in a two-dimensional space. In dynamics, polar coordinates are often converted to Cartesian coordinates to simplify calculations and allow for easier comparison with results from other physical laws and principles.

What are some real-world applications of dynamics in the polar coordinate system?

Dynamics in the polar coordinate system is used in many real-world applications, such as analyzing the motion of planets and satellites in orbit, determining the trajectory of projectiles, and designing circular motion systems, such as amusement park rides and roller coasters. It is also essential in fields like aerospace engineering, robotics, and navigation systems.

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