Angular speed, linear speed, and linear speed at halfway point.

Jul 2015
705
25
United States
rpm = 500 ; r=45cm



(A) Angular Speed:

to find the angular speed in units of radian/seconds I know the radian measure of a circle which is 2pirad...

then 500 rev/60 secs x 2pirad/1rev

I get the answer 52.35 cm

but they are getting the answer 50pi/3?? I have no idea how they are getting that.

(B) Find the linear speed, in units of cm/sec.

C=2pi(45)
C=90pi
therefore 1 rev = 90picm

500 rev/60 sec x 90picm/1 rev

then I get the answer 2356.19 cm/sec

and they get 750 pi???

and for (C) All you have to do is divide by two which is obvious, and therefore it is 375 pi.

What am I doing wrong??? Please explain to me what angular speed is and what linear speed is? TYVM
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
(a) $\omega = \dfrac{500 \, rev}{min} \cdot \dfrac{2\pi \, rad}{rev} \cdot \dfrac{1 \, min}{60 \, sec} = \dfrac{1000\pi}{60} = \dfrac{50\pi}{3} \, rad/sec$


(b) $v = r\omega$
 
Jun 2008
1,389
513
Illinois
then 500 rev/60 secs x 2pirad/1rev

I get the answer 52.35 cm

but they are getting the answer 50pi/3?? I have no idea how they are getting that.
You have the same answer as the book, just wrong units - angular speed is radians/s, not cm/s:

\(\displaystyle \frac {500 \ rev}{60 \ s} \times \frac {2 \pi \ rad}{rev} = \frac {500 \pi}{30} \frac {rad} s = 52.35 \frac {rad} s\).

(B) Find the linear speed, in units of cm/sec.

C=2pi(45)
C=90pi
therefore 1 rev = 90picm

500 rev/60 sec x 90picm/1 rev

then I get the answer 2356.19 cm/sec

and they get 750 pi???
Again - your answer agrees with the book, because \(\displaystyle 750 \pi \ cm/s= 2356 \ cm/s\)