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

In summary, in a revolving system where a ball is tied to a wire with no mass and given a certain velocity, the length of the wire will affect the change in angle with respect to time, or the angular velocity. This means that a longer wire will result in a smaller angle. This may not align with intuition, but it can be explained by considering the increase in path length and decrease in radians traversed in one second.
  • #1
Tali
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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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  • #2
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.
 
  • #3
Tx. It answers my question
 

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

1. Does the length of the wire affect the angle?

Yes, the length of the wire can affect the angle in certain scenarios. If the wire is being used as a pendulum, for example, the length of the wire will impact the period and therefore, the angle at which it swings. In other cases, such as a wire being used to measure tension, the length of the wire may not have a significant impact on the angle.

2. How does the length of the wire impact the angle?

The exact impact of the length of the wire on the angle will depend on the specific situation. In general, a longer wire will result in a larger angle, and a shorter wire will result in a smaller angle. This is because the length of the wire is one factor that affects the forces acting on it, such as gravity or tension.

3. Is there an ideal length for a wire to achieve a specific angle?

It depends on the desired angle and the specific setup. In some cases, there may be an ideal length that will result in the desired angle due to the forces acting on the wire. In other cases, the length may not have a significant impact on the angle. It is important to carefully consider the setup and the forces involved when determining the ideal length for a wire.

4. Can the angle be changed by adjusting the length of the wire?

Yes, adjusting the length of the wire can change the angle in many cases. This is because the length of the wire is one factor that affects the forces acting on it, and changing the length can alter the balance of forces. However, there may be other factors at play that can also impact the angle, so it is important to consider all variables when making adjustments.

5. How do I calculate the impact of the wire length on the angle?

The impact of the wire length on the angle can be calculated by considering the forces involved and using relevant equations, such as Newton's laws of motion or equations for pendulum motion. It is important to carefully consider all factors and variables in order to accurately calculate the impact of the wire length on the angle.

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