Understqarnding equations for angular velocity

[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 that's it? or is there more. if there is more, then why doesn't 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. I am soo lost. hahaha

thanks guys

 

[PhanthomJay]

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 that's it? or is there more. if there is more, then why doesn't 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. I am soo lost. hahaha

thanks guys

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?

 

[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

 

[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. I am struggling and need encouragement. haha. i did do algerbra last semester but that is no where near trig.

thank you sooooooooooooo much

 

[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.

 

[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