# TrigonometryAngular Velocity

#### didaw

##### New member
(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.

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 dont know what it means by radians can any one help me out i would realy appreciate it?

#### skeeter

##### Well-known member
MHB Math Helper
Re: Need help urgently would realy 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.

#### didaw

##### New member
Re: Need help urgently would realy appreciate any help regarding Angular Velocity

im confused because i dont have the arc length so i wont be able to work out the angle? the formular for the arc length is angle x pi x r / 180 and to work out the area its s x r / 2

#### didaw

##### New member
Re: Need help urgently would realy 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

#### didaw

##### New member
Re: Need help urgently would realy appreciate any help regarding Angular Velocity

Thank you!