Does the Variable ##t## Represent Multiple Concepts in Physics Problems?

In summary, the variable \( t \) in physics problems often represents time, but it can also denote other concepts depending on the context, such as temperature or tension. The use of \( t \) varies based on the specific discipline or scenario being analyzed, highlighting the importance of understanding the context in which it is applied to avoid confusion. Careful attention to definitions and units is essential for accurate problem-solving in physics.
  • #1
kanekiyura
1
0
Homework Statement
A rigid thin ring shaped like a circle of radius R rotates
uniformly around a fixed axis passing through one of the points of the circle and perpendicular to its plane. An ant crawls along the ring, moving all the time relative to the annulus with a constant velocity.At time t = 0, the velocity of the ant relative to a stationary observer is maximal and equal to v1.After time t, this velocity becomes minimal for the first time and equal to v2. Find the law of variation of the velocity value v(t).
Relevant Equations
I really don't know
I do not know how to solve this. All I got was to exclude the speed of the ant relative to the ring from the equation for its full speed
 
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  • #2
Hello @kanekiyura ,
:welcome:​

Unfortunately, PF doesn't work this way. The PF guidelines dictate that you post your best attempt at solution before we are allowed to help.

Make some sketches that help you find ##v_1## and ##v_2##.

##\ ##
 
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  • #3
First, to be accurate, it's the ant's speed that can be constant relative to the periphery of the ring, not its velocity. The velocity keeps changing direction.
Can you write an equation for the velocity of the centre of the ring at time t? And an equation for the ant's velocity relative to the centre of the ring?
 
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  • #4
kanekiyura said:
After time t, this velocity becomes minimal for the first time and equal to v2. Find the law of variation of the velocity value v(t).
Is there consensus that symbol ##t## is used rather carelessly to stand for two different entities?
1. A specific time at which the "velocity becomes minimal for the first time and equal to v2."
2. The independent variable in "the law of variation of the velocity value v(t)."

If that is the case, then perhaps a clearer formulation of the relevant section might be

At time ##t = 0##, the velocity of the ant relative to a stationary observer is maximal and equal to ##v_1.## At time ##t=t_2## this velocity becomes minimal and equal to ##v_2##. Find the law of variation of the velocity ##v(t).##
 
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FAQ: Does the Variable ##t## Represent Multiple Concepts in Physics Problems?

Does the variable ##t## always represent time in physics problems?

No, while ##t## most commonly represents time in physics problems, it can represent other concepts depending on the context. For example, in thermodynamics, ##t## might represent temperature, and in certain mathematical contexts, it could be used as a parameter for curves or functions.

How can I determine what ##t## represents in a given physics problem?

To determine what ##t## represents, you should carefully read the problem statement and any accompanying explanations or diagrams. The context of the problem and the units associated with ##t## can provide significant clues. Additionally, checking the definitions and conventions used in the specific field of study can help clarify its meaning.

Are there standard conventions for using ##t## in different branches of physics?

Yes, there are standard conventions, but they can vary between different branches of physics. For example, in classical mechanics and relativity, ##t## typically represents time. In thermodynamics, it might represent temperature. However, these conventions are not absolute, and it's essential to rely on the context and problem statement to understand the specific usage.

Can ##t## represent multiple concepts within the same problem?

It's uncommon but possible for ##t## to represent multiple concepts within the same problem. If this occurs, the problem should clearly define each usage and context to avoid confusion. Typically, different symbols or subscripts are used to distinguish between the different concepts to maintain clarity.

What should I do if I am unsure about what ##t## represents in a problem?

If you are unsure about what ##t## represents, you should review the problem statement and any provided materials for definitions or context clues. If the problem is part of a textbook or academic paper, consulting the introductory sections or appendices may help. When in doubt, asking a teacher, professor, or colleague for clarification is also a good approach.

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