Need help urgently would realy appreciate any help regarding Angular Velocity

[didaw]

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

 

[Dr.Peterson]

First, "pie" is a pastry; you're referring to "pi", the name of a Greek letter.

Now, you say your only difficulty is not knowing what radians are? Does this not come from a textbook that defines them? If not, search! Here's one place to learn about them: https://www.mathsisfun.com/geometry/radians.html

 

[tkhunny]

pie is for eating.
pi is for math

Go to some effort to be a little more organized.

[math]\dfrac{2100\;rev}{3\;min}\cdot\dfrac{2\pi\;rad}{1\;rev}\cdot\dfrac{1\;min}{60\;sec}\;=[/math]
Careful with "radians". They aren't real units.

 

[didaw]

First, "pie" is a pastry; you're referring to "pi", the name of a Greek letter.

Now, you say your only difficulty is not knowing what radians are? Does this not come from a textbook that defines them? If not, search! Here's one place to learn about them: https://www.mathsisfun.com/geometry/radians.html

I've figured it out I did spend hours searching. I wanted to know what pi / 3 radian ment. I thought it pi / 3 X something bit it's just pi / 3 = 1.046 radian, then you convert that to degrees.

 

[topsquark]

This is something I try to work on with my Physics students. As tkhunny mentioned, the unit radians = rad is a bit strange in the sense that it is actually unitless. (1 rad = 1 m /1 m by definition.) However in order to refer to an angular measure it needs to be there to designate it as an angle. So what you wanted to say above is \(\displaystyle \pi\)/3 rad = 1.046 rad. And \(\displaystyle \pi\) rad = 180 degrees. etc.

-Dan

 

[pka]

Careful with "radians". They aren't real units.

I completely disagree with that statement. In fact it is the very opposite.
Radians are real numbers. One radian is the measure of any central angle that intercepts an arc of length equal to the radius of the circle.
Now tell us what is a degree? It appears that 360 is a primitive approximate count for a full year in which the four seasons.
Historically that is the origin of degrees. Hence degrees are vague at best.

 

[topsquark]

This is true but I sympathize with tkhunny's comment. Consider torque. Depending on how you calculate it it has units of Nm or Nm-rad. Properly speaking it has to be Nm-rad as anything with the units Nm is an energy, not a torque. We need the rad unit in there somewhere but one equation for torque can be shown to be equivalent to the other, so the units should be the same.

rad pops in and out of Physics units at will, it seems. I once tried to come up with a fix for it but eventually gave up.

-Dan

 

[tkhunny]

I completely disagree with that statement. In fact it is the very opposite.
Radians are real numbers. One radian is the measure of any central angle that intercepts an arc of length equal to the radius of the circle.
Now tell us what is a degree? It appears that 360 is a primitive approximate count for a full year in which the four seasons.
Historically that is the origin of degrees. Hence degrees are vague at best.

I stand only by my ability to raise the conversation. And there it is.