• theBEAST
In summary, the conversation discusses the direction of the force vector in a free body diagram and the confusion surrounding whether it should be in the tangential or theta direction. It is clarified that the tangential direction is perpendicular to the normal direction and that the force from the rod must be normal to the surface of the rod. It is also mentioned that the net force on the particle would be in the tangential direction.
theBEAST

## Homework Statement

Here is a picture of the problem with the free body diagram:
http://dl.dropbox.com/u/64325990/HW%20Pictures/problem101.PNG

I am confused about why the free body diagram has the force vector in the direction of the aθ. When I did it I thought the force that the rod would exert on the particle would be in the tangential direction? In other words in the direction of at.

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I don't see a_t in your pic.

But anyway, I am pretty sure that the tangential direction is the theta direction as well.
So a_theta = a_t

In polar coordinates the radial direction is out from the origin, and the theta direction is perpendicular to that, which would be the tangential direction.

spacelike said:
I don't see a_t in your pic.

But anyway, I am pretty sure that the tangential direction is the theta direction as well.
So a_theta = a_t

In polar coordinates the radial direction is out from the origin, and the theta direction is perpendicular to that, which would be the tangential direction.

No the unit vector in the tangential direction (u_t) is perpendicular to the normal direction. a_theta != a_t..

I edited the picture slightly to show the direction of a_t which is in the direction of it's unit vector u_t.

i'll just add this to what spacelike says …

in polar coordinates, the actual coordinates are r,θ,

and so the unit vectors for increasing r (with fixed θ), and for increasing θ (with fixed r) are called er and eθ, respectively

(or $\boldsymbol{\hat{r}}$ and $\boldsymbol{\hat{θ}}$)

and their velocity or acceleration components therefore have the same subscripts

(and of course, t isn't a coordinate )

I think I understand your confusion. There are two tangential vectors you could define. One would be the vector that is tangential to the motion of the particle and the other is tangential to any point on the rod which is rotating (but at a constant distance from the origin). The second one must be in the theta direction which is perp. to the rod. The force from the rod MUST be that force which is normal to the surface of the rod. Unless there are strange things going on, the only interaction between the rod and particle must be normal to the rod. The force that you are thinking about that would be in the $u_t$ direction is the net force on the particle. If that were asked, you would be correct.

## 1. What is the difference between tangential and radial coordinate problem?

The tangential coordinate problem involves finding the position of an object along a tangent line, while the radial coordinate problem involves finding the distance of an object from a central point. In simpler terms, the tangential coordinate problem deals with the horizontal position of an object, while the radial coordinate problem deals with the vertical position.

## 2. How do I know when to use the tangential coordinate versus the radial coordinate?

The type of coordinate to use depends on the specific problem you are trying to solve. If you are dealing with a circular motion or a problem involving rotation, the radial coordinate would be more appropriate. If you are dealing with motion in a straight line, the tangential coordinate would be more applicable.

## 3. What is the FBD (Free Body Diagram) and how does it relate to tangential and radial coordinate problems?

The FBD is a visual representation of the forces acting on an object in a problem. It is used to help solve problems involving motion and can be used in both tangential and radial coordinate problems. It helps to identify and analyze the forces acting on an object and their direction, which aids in finding the solution.

## 4. How do I solve a tangential and radial coordinate problem?

The first step is to draw an accurate FBD of the object in question. Then, identify the forces acting on the object and their direction. Next, use the appropriate equations for tangential or radial motion to solve for the unknown variables. It is important to pay attention to units and use the correct formula for the given problem.

## 5. What are some common mistakes when solving tangential and radial coordinate problems?

Some common mistakes include using the wrong formula or equation, not considering all the forces acting on the object, and not paying attention to units. It is also important to draw an accurate FBD and to remember the difference between tangential and radial coordinates. Additionally, it is important to check your work and make sure the answer makes sense in the context of the problem.

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