How Do You Calculate Angular Velocity for a Spinning Engine?

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  • #1
Similis
Hi

Can someone help me to demonstrate the 2 followed relations.

The dispositif is an engine who spin around himself

ώ = 2.(pi)/T

ώ is the angular velocity

thx and sorry for my bad english
 
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  • #2
Is that supposed to be [tex]\dot \omega[/tex] as in [tex]\frac{d \omega}{dt}[/tex]? I assume not.

I think that you are just trying to show that if
[tex]\omega = 2 \pi f[/tex]
where [tex]\omega[/tex] is the angular frequency and f is the frequency, then an equivalent way of writing it is
[tex]\omega = \frac{2 \pi}{T}[/tex]
using the relationship that [tex]f = 1/T[/tex]
 
  • #3


Hello,

I would be happy to assist you with demonstrating the two relations you mentioned. The first relation, ώ = 2.(pi)/T, is known as the angular velocity equation. This equation represents the angular velocity, ώ, of an object spinning around an axis in radians per second. The value of 2.(pi) represents the circumference of a circle, and T represents the time it takes for the object to complete one full rotation.

To demonstrate this relation, we can use an example. Let's say we have a wheel that takes 5 seconds to make one full rotation. We can plug this value into the equation and solve for ώ:

ώ = 2.(pi)/T
ώ = 2.(pi)/5
ώ = 0.4(pi) radians per second

This means that the wheel is spinning at a rate of 0.4(pi) radians per second. We can also convert this to revolutions per minute (RPM) by multiplying by 60 seconds:

0.4(pi) radians per second x 60 seconds = 24(pi) RPM

The second relation you mentioned, the dispositif, is an engine that spins around itself. This can also be represented by the angular velocity equation, where the time it takes for one full rotation, T, is equal to the period of the engine. The period is the time it takes for the engine to complete one cycle or rotation.

I hope this helps to demonstrate the relations you were looking for. If you have any further questions or need clarification, please let me know. And your English is just fine, no need to apologize! Science is a universal language.
 

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