# Understqarnding equations for angular velocity

1. Sep 20, 2011

### LT72884

I am having dificulty understanding the equation to angular velocity.

w=alpha/time

so if given this statement, (this is not homework). A helicopter blade is rotating at 400 rev per minute, find angular velocity in radians per minute.

So i have w=400/1 minute. great, so thats it? or is there more. if there is more, then why doesnt the equation state that. What am i supposed to do with 400/1? to me, that should be the answer because we did indeed find that w=alpha over time where alpha is 400 and time is 1 minute. im soo lost. hahaha

thanks guys

2. Sep 20, 2011

### PhanthomJay

For constant angular velocity, w = angular displacement/time. For constant angular acceleration starting from rest, w = alpha*time, where alpha is the angular acceleration.

Your problem relates to constant angular velocity. You are correct in that it's angular velocity is 400 rev/min. But the problem asks you to convert it to radians/minute. So how many radians in a revolution?

3. Sep 20, 2011

### daqddyo1

Angular velocity is usually measured in radians per second. In one rotation the angle swept out is 360 degrees or 2xpi radians. So, if the rate of rotation is 400/minute, then the angular velocity would be 400 x 2xpi radians per minute which would be 800pi/60 = 40pi/3 radians/second.

Hope this helps,

John

4. Sep 20, 2011

### LT72884

arg, this whole radians thing confuses me. lol. so because it asked for it in radians, i use 2pi because in one revolution is 360* or 2pi. So is arc length related to this equation at all? please be easy. this is my first trig calss and i have not had math since 2002. please please be easy on me. im struggling and need encouragement. haha. i did do algerbra last semester but that is no where near trig.

thank you sooooooooooooo much

5. Sep 20, 2011

### olivermsun

Radians are 2*pi for a circle because that's the total arc length around the unit circle (radius = 1). When you scale it to a larger circle, then the arc length is just angle in radians * radius.

6. Sep 22, 2011

### daqddyo1

Re radians, imagine an isoceles triangle ABC (AB=AC) drawn inside a circle with point A at the centre and B and C are points on the circumference of that circle.
Replace side BC with the arc between B and C.

If the length of this arc = AB or AC, then the angle BAC is defined as 1 radian regardless of the length of AB.

daqddyo1