In mechanics: doea the length of the wire affects the angle?

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SUMMARY

The length of a wire directly affects the angle of a ball tied to it when considering a tension system with constant velocity. Specifically, as the length of the wire increases, the angle decreases due to the relationship between angular velocity and the radius of the circular path. This conclusion is derived from energy principles and the mechanics of revolving systems, confirming that a longer wire results in a slower angular displacement over time.

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  • Understanding of basic mechanics and tension forces
  • Familiarity with angular velocity concepts
  • Knowledge of energy conservation principles in physics
  • Experience with circular motion dynamics
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  • Study the relationship between angular velocity and radius in circular motion
  • Explore energy conservation in revolving systems
  • Investigate the effects of tension on angular displacement
  • Learn about the mathematical modeling of pendulum motion
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Homework Statement


general question: if I give a ball velocity (He is tied to a wire (tension)) and consider that the wire has no mass. Does the length of the wire affects the angle?
If I solve this with energy tools then I get that the longer the wire the smaller the angle.
it does not settle down with my intuitaion.
can someone please explain.

Homework Equations

The Attempt at a Solution

 
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The length of the wire will affect your change in angle with respect to time, or your angular velocity.
You are describing a revolving-type system where the wire causes the ball to revolve around the center, right?
Think of it this way, if speed is constant, the path increases with the length of the wire, and so the number of radians traversed in one second would decrease as the length of the wire increased.
Does this address your question? If not, please clarify.
 
Tx. It answers my question
 

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