MHB Angular Velocity - 2100 Revs in 3 Mins - 73.3 Rad/s

AI Thread Summary
The discussion revolves around calculating the average angular velocity of a rotating machine shaft, which is determined to be 73.3 rad/s after converting 2100 revolutions in 3 minutes to radians. Participants clarify the concept of radians, explaining that an angle in radians is defined as the arc length divided by the radius. The formulas for arc length and sector area are provided, emphasizing that the angle must be in radians for accurate calculations. A participant expresses confusion about calculating the minor sector angle due to not having the arc length, but later realizes that pi/3 radians corresponds to 60 degrees. The thread concludes with a participant expressing gratitude for the clarification.
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(i) A rotating machine shaft turns through 2100 revolutions in 3 minutes. Determine the average angular velocity, w, of the machine shaft in rad/s.

the answer for this is

2100 x 2 pie = 4200 pie radian

3 mins = 180 seconds

4200 / 180 = 73.3 rad/s
(ii) Determine the area and arc length of the minor sector shown here for the 120mm diameter circle.

minor section angle = pie / 3 x radians (this question is formatted as pie with a line under it then 3 under the line and radians next to it so i am presuming that i have to x it)
i know how to work out everything apart from the minor section angle i just don't know what it means by radians can anyone help me out i would really appreciate it?
 
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Re: Need help urgently would really appreciate any help regarding Angular Velocity

an angle, $\theta$, in radian measure is $\theta = \dfrac{s}{r}$ where $s$ is the arc length subtended by the central angle and $r$ is the radius. (see diagram)

In short, there are $2\pi$ radians in an entire circle because $C = 2\pi r$ where $r = 1$

(btw, $\pi$ is spelled "pi" ... "pie" is something you eat.)

So ...

half a circle = 180 degrees = pi radians

quarter of a circle = 90 degrees = pi/2 radians

sixth of a circle = 60 degrees = pi/3 radians

eighth of a circle = 45 degrees = pi/4 radians

etc ...

(ii) Determine the area and arc length of the minor sector shown here for the 120mm diameter circle.

arc length, $s = r \cdot \theta$ where $r$ is the radius.

sector area, $A = \dfrac{\theta}{2\pi} \cdot \pi r^2 = \dfrac{\theta \cdot r^2}{2}$

Note that both of the above formulas only work if the central angle, $\theta$, is in radians.
 
Re: Need help urgently would really appreciate any help regarding Angular Velocity

im confused because i don't have the arc length so i won't be able to work out the angle? the formula for the arc length is angle x pi x r / 180 and to work out the area its s x r / 2
 
Re: Need help urgently would really appreciate any help regarding Angular Velocity

ahh i get it so pi / 3 radans is 60 degrees. i was thinking i had to do something fancy with it
 
Re: Need help urgently would really appreciate any help regarding Angular Velocity

Thank you!
 
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