How Do Angular Velocities Remain Constant With Different Radii?

[Benjamin_harsh]

Homework Statement

Figure shows a wheel rotating about $O_{2}$. Two points A
and B located along the radius of wheel have speeds
of 80 m/sec and 140 m/sec respectively. The distance between
the points A and B is 300mm. The diameter of the wheel (in mm) is:

Relevant Equations

$ω_{A} = ω_{B}$

$V = ωR$

$ω = \large \frac {V}{R}$

$ω_{A} = ω_{B}$

$\large \frac {V_{A}}{R - 0.3} = \frac {V_{b}}{R}$

$\large \frac {80}{R - 0.3} = \frac {140}{R}$

$R = 0.7 m$

Diameter = $0.7*2 = 1.4m = 1400mm$

 

[scottdave]

Do you know the meaning of omega? This is the angular velocity. Normally this is radians per second, but you could think of it in other units, such as revolutions per minute. If the outer rim (point B) makes 10 revolutions in a minute, for example, how many revolutions does point A make in a minute?

 

[Benjamin_harsh]

If the outer rim (point B) makes 10 revolutions in a minute, for example, how many revolutions does point A make in a minute?

same 10 revolutions in a minute. Am I right?

 

[scottdave]

same 10 revolutions in a minute. Am I right?

Yes, so 1 revolution is 360° or 2π radians, so do you see now how each point travels the same number of radians per second?

 

[Benjamin_harsh]

Yes, so 1 revolution is 360° or 2π radians, so do you see now how each point travels the same number of radians per second?

So answer is $\frac {360}{60}$? I mean 1 min = 60 sec.

 

[scottdave]

So answer is $\frac {360}{60}$? I mean 1 min = 60 sec.

I'm not sure what you are asking here. You solved the initial problem correctly. I was just giving an example to help show you how the angular velocity is constant along the wheel.