Angular velocity and acceleration

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SUMMARY

The discussion focuses on calculating angular velocity and acceleration for a mass sliding within a vertical circular tube, connected to a spring. The key equations utilized include conservation of energy and Newton's second law, specifically addressing the forces acting on the mass. The participant identifies an error in their approach regarding the spring's force direction, indicating a misunderstanding of the forces involved in the system.

PREREQUISITES
  • Understanding of angular motion and forces in circular motion
  • Familiarity with conservation of energy principles
  • Knowledge of Newton's second law of motion
  • Basic concepts of spring mechanics and Hooke's law
NEXT STEPS
  • Study the derivation of angular velocity in circular motion
  • Learn about the application of conservation of energy in dynamic systems
  • Explore the effects of spring forces in circular motion scenarios
  • Investigate the relationship between angular acceleration and net forces
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and tutors seeking to clarify concepts related to angular motion and spring dynamics.

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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

-------

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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