Emergency problem

  • Thread starter ShayanJ
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  • #1
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There is a rod rotating around the z axis with angular velocity [itex] \omega [/itex].The angle between the rod and z axis is constant and equal to [itex] \alpha [/itex].A mass m is constrained to move on the rod.The gravitational force is in the negative direction of z axis and the friction between the mass and rod is negligible.At time t=0 , the mass is at distance [itex] r_{0} [/itex] from the origin and is stationary relative to rod.

1-In a proper coordinate system,write the newton's second law for the mass in a inertial frame of reference and write the differential equations of motion.Highlight the expressions indicating the reaction of rod.

2-Solve the differential equations and write the mass's distance from origin as a function of time.

3-Calculate the reaction force of the rod(direction and magnitude)


thanks
 

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  • #2
Spinnor
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Does the following get you started?
 

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  • #3
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Thanks alot.My mistake was that I didn't write N but only the centripetal force.

But it seems sth is wrong there.Just imagine such a thing not rotating.you know that the mass slides down.So it seems that [itex] N \sin {\alpha} [/itex] is not equal to mg.
Another question.
Last night I worked on it and got some things but there is a big puzzle in my mind.
Textbooks say that the acceleration in spherical coordinates is as following:

[itex] \textbf{a}=(\ddot{r} - r \dot{\phi}^{2} \sin ^ {2} \theta -r \dot{\theta}^{2}) \hat{e_{r}} + [/itex] [itex] ( r \ddot{\theta} + 2 \dot{r} \dot{\theta} - r \dot{\phi} ^ {2} \sin {\theta} \cos{\theta}) \hat{e_{\theta}} + [/itex] [itex] (r \ddot{\phi} \sin{\theta} + 2 \dot {r} \dot {\phi} \sin {\theta} + 2 r \dot{\theta} \dot{\phi} \cos{\theta}) \hat{e_{\phi}}
[/itex]

Shoud I use the r coordinate of the above equation for writing Newton's 2nd law or simply write [itex] m \ddot{r} [/itex] ?
I tried both.When I use the equation above I get crazy things.But when I use [itex] m \ddot{r} [/itex] I get a cosine.
I'm just wondering that the above equation is the most general and can't understand why it becomes wrong in this problem.

The last question.
The [itex] \theta [/itex] coordinate of the acceleration should be zero.But when I write the Newton's 2nd law in that coordinate and replace [itex] \ddot{\theta} [/itex] with zero,I get r=constant,which is clearly wrong.Could you write that?

thanks
 
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  • #4
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Do you know what i said?
 

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