Finding Acceleration in a Rotating Tube

In summary, a cylindrical particle placed in a frictionless tube can slide back and forth. If the particle is not positioned in the centre of the tube, the acceleration along the tube can be determined using the equation a_r = r "doubledot" - r x U^2, where r is the distance between the particle and the centre of the tube. To find r "doubledot", a function representing the distance r needs to be differentiated twice. However, since no function was provided, the tangential velocity, v, can be used as it is equal to the angular velocity, w, times the radius, r. Therefore, the formula a = r double dot - r*w^2 can be simplified to a
  • #1
Plastik
5
0
Question goes something like:
A cylindrical particle is placed in a certain metre long, frictionless tube, where it can slide back and forth. If the particle is not positioned in the centre of the tube, then as the tube is turning at a constant angular velocity of U, determine the acceleration of the particle along the tube.

I understand from my textbook that the equation to use in such case should be
a_r = r "doubledot" (second derivative w.r.t time) - r x U^2
where r = the distance between the particle to the centre of the tube.

But I do not know how to work out r "doubledot".

Any help is much appreciated.
 
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  • #2
you need a function that represents the distance r so you can differentiate it twice to get the acceleration (which is r double dot)
 
  • #3
But I wasn't provided with any sort of function in relation to r. It's just a particle sliding inside a tube. ><
 
  • #4
ah ok sorry i didnt see the angular velocity bit.

ok

Tangental velocity, v, is equal to angular velocity, w, times radius, r. Ie v/r = w. So if centripetal acceleration, a, is (v^2)/r you should be able to work out a in terms of r and/or w
 
  • #5
Oh orite.

So what do I do with the formula

a = r double dot - r*w^2?

can I just ignore it and use a = r*w^2 instead?
 
  • #6
its the same thing :) r double dot is simply the 2nd time derivative of r, which being a spatial value, is acceleration of that value.
 

1. What are polar coordinates of motion?

Polar coordinates of motion are a type of coordinate system used to describe the position and movement of an object in two-dimensional space. They use a distance (r) and an angle (θ) to locate a point in relation to a fixed origin.

2. How do polar coordinates of motion differ from Cartesian coordinates?

In Cartesian coordinates, the position of a point is described using an x-coordinate and a y-coordinate. In polar coordinates, the position of a point is described using a distance (r) and an angle (θ) from the origin. This allows for a more intuitive representation of circular motion.

3. How are polar coordinates of motion used in physics?

Polar coordinates of motion are commonly used in physics to describe circular or rotational motion, such as the movement of a pendulum or a planet around the sun. They are also used in fields such as fluid dynamics and electromagnetism.

4. What are the advantages of using polar coordinates of motion?

One advantage of using polar coordinates of motion is that they provide a simpler and more intuitive representation of circular motion compared to Cartesian coordinates. They also make it easier to describe and analyze motion in fields such as physics and engineering.

5. How are polar coordinates of motion converted to Cartesian coordinates?

Polar coordinates of motion can be converted to Cartesian coordinates using the equations x = rcos(θ) and y = rsin(θ). This allows for a transformation between the two coordinate systems, making it easier to analyze and compare different types of motion.

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