Circular Motion and resultant force

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SUMMARY

The discussion focuses on calculating angular velocity in circular motion while considering the effects of friction. The key equation used is F = mv²/r, where the resultant force is expressed as the difference between centripetal force and frictional force. The solution derives angular velocity as angular vel = (g * meu / x)^(1/2), effectively linking gravitational force, friction coefficient, and radius of motion. The conversation emphasizes the importance of identifying forces acting on the mass to accurately determine acceleration.

PREREQUISITES
  • Understanding of circular motion dynamics
  • Familiarity with Newton's laws of motion
  • Knowledge of friction coefficients (meu)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of centripetal acceleration in circular motion
  • Learn about the effects of friction in rotational systems
  • Explore the relationship between angular velocity and linear velocity
  • Investigate the implications of inertial frames in physics
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to clarify concepts related to forces and motion.

Priyadarshini
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Homework Statement



WP_20160129_22_51_42_Pro.jpg

Homework Equations


F= mv^2/r
v = angular vel* r

The Attempt at a Solution


resultant force= ma-frictional force
= mv^2/r - mg*meu
= (angular vel)^2mx - mg*meu
But then how do I get the angular speed when I don;2 know the resultant force?
 
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Priyadarshini said:
resultant force= ma-frictional force
Only one (horizontal) force acts on the mass.
 
Doc Al said:
Only one (horizontal) force acts on the mass.
I don't understand.
 
Priyadarshini said:
I don't understand.
Please identify the forces acting on the mass.
 
Doc Al said:
Please identify the forces acting on the mass.
There is no centripetal force as the mass is not accelerating.
There is the friction force and centrifugal force
 
Priyadarshini said:
There is no centripetal force as the mass is not accelerating.
There is the friction force and centrifugal force
That would be true if viewed from the rotating frame, which requires the inertial centrifugal force. If so, what is the acceleration?

Or you can view it from the usual inertial frame, where the only force would be friction and there would be a centripetal acceleration.
 
Doc Al said:
That would be true if viewed from the rotating frame, which requires the inertial centrifugal force. If so, what is the acceleration?

Or you can view it from the usual inertial frame, where the only force would be friction and there would be a centripetal acceleration.

so F=mv^2/r
mv^2/r=N*meu
v*angular vel* m = mg*meu
so angular vel = g*meu/v
as v= angular vel* x
angular vel^2=g*meu/x
so angular vel = (g*meu/x)^(1/2)
Which is the answer, thank you!
 

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