How Do You Convert Angular Velocity to RPM?

[blackice552]

1. Homework Statement
theta(t) = 2t^3 + 5t^2 - 2t + 1

Find the angular velocity in rpm's at t = 2s if the radius of the circular path is 30 cm

Basically I want to kno if i did this part of the problem right b/c my professor didn't give us a key for the practice exam



2. Homework Equations
omega = d theta/dt


3. The attempt at a solutio
omega(t) = 6t^2 + 10t -2
omega(2) =42 m/s
30 cm = .3 m
Circumference = .3(2)pi = .6pi
42 m/s * 60s/min = 252 m/min
252 m/min * 1 rev/.6pi m = 42/pi rpm

 

[ziad1985]

omega(2) = 42 (deg or rad)/s depends on the unit used..
if you have the the angular velocity all you need to find how much rpm: is to divide 2*pi by omega(to find out how much it takes to make a full turn aka 2*pi) and then see how many round in one minute..
Edit:Btw it's either 2*pi or 360 depends on unit used..

 

[blackice552]

omega(2) is rad sorry

 

[ziad1985]

Did you understand what I said?
do you need me to explain more?

 

[blackice552]

could u please explain a little more

 

[ziad1985]

you have calculated that at t=2 the angular speed is 42 rad/s
you know that rpm means round per minute.
a round is equivalent to what? it's equivalent to a full trip around that circle, that means it must goes through a 2*pi(360 degree) trip to return from where it started.
now since you know the angular speed, and you know the angle 2*pi, you can calculate how much time is needed to make that trip..
hence you can calculate how many trips can be done in one minute, if you know how much time is needed to make one round

 

[blackice552]

so the radius of 30 cm has nothing to do with it? I thought the circumference would be the round

 

[ziad1985]

you have the angular speed , not the linear speed, you know how much the angle is changing per second , not how much distance per second(although it's easy to calculate it)

I thought the circumference would be the round

so? unless you want to use the linear speed , the circumference have no use to calculate the rpm..
what part you need more explaining?

 

[blackice552]

i think i understand now so intead of dividing by the circumference like i was doing all i have to do is divide by 2 pi

 

[ziad1985]

yes divide the angular speed by 2pi to calculate how much time does it need to turn 2pi which is equivalent to one round...

 

[blackice552]

thanks for the help