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

• MHB
• didaw1
In summary, the average angular velocity of the rotating machine shaft is 73.3 rad/s. For the minor sector shown in the 120mm diameter circle, the angle in radians can be calculated using the formula $\theta = \dfrac{s}{r}$, where $s$ is the arc length and $r$ is the radius. The sector area can be calculated using the formula $A = \dfrac{\theta \cdot r^2}{2}$, where $r$ is the radius and $\theta$ is in radians. The formulas for arc length and sector area only work if the central angle is in radians.
didaw1
(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 don't know what it means by radians can anyone help me out i would really appreciate it?

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!

## 1. What is angular velocity?

Angular velocity is a measure of the rate of change of angular displacement over time. It is commonly expressed in units of radians per second (rad/s).

## 2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It can also be calculated by dividing the total number of revolutions by the total time taken.

## 3. What does 2100 revs in 3 mins mean in terms of angular velocity?

2100 revs in 3 mins means that the object has completed 2100 revolutions in 3 minutes. This corresponds to an angular displacement of 2100 x 2π = 13,200π radians. Dividing this by 3 minutes gives an angular velocity of 73.3 rad/s.

## 4. How does angular velocity relate to linear velocity?

Angular velocity and linear velocity are related by the radius of the object's circular motion. The linear velocity is equal to the angular velocity multiplied by the radius of the circle.

## 5. What factors can affect angular velocity?

Angular velocity can be affected by changes in the radius of the circular motion, changes in the object's mass or distribution of mass, and external forces such as friction or air resistance. It can also be affected by changes in the object's initial angular velocity.

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