Angular velocity and acceleration

AI Thread Summary
The discussion revolves around calculating the angular velocity and acceleration of a mass sliding in a vertical circular tube connected to a spring. The conservation of energy and Newton's second law are applied to derive the equations governing the system's motion. A mistake is noted in the initial attempt, specifically regarding the treatment of the spring's force direction. The importance of correctly incorporating the spring's force into the equations is emphasized for accurate results. Clarification and corrections on the calculations are sought to resolve the issue.
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Homework Statement



the spring oa is fixed from one end o to the bottom of a vertical circular smooth tube and from its other end to a slider a of mass m which can slide smoothly along the tube initially started from rest at a .
find :
i) angular velocity
II) angular acceleration at any angle
iii)angle at which the slider comes to instantaneous rest

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Homework Equations



Conservation of energy and netwen 2nd law

1/2 mv^2 + 1/2 Kx^2 + mgh=1/2 mv^2 + 1/2 Kx^2 + mgh

The Attempt at a Solution



fn=fan = mrΘdot = n-mgcosΘ +kx
ft=f at = mrΘt double dot = -mgsinΘ

Θ(dot)^2 = 2mgcosΘ + 2gr

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i think i made a mistake & hope someone can help with this situation
 
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I'd like to see your working for your attempted solution. The fact that you have kx appearing in your expression for fn but not adding a component to ft suggests that you are viewing the spring's force as directed towards the circle's centre. It isn't.
 
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