Angular Speed

**suspenc3** · Nov30-05, 04:04 PM

Hi,

A flywheel with a diameter of 1.2 m is rotating at an angular speed of 200 revs/min

What is the angular speed of the flywheel in radians per second?

Would I just do this?

200 revs/min = 3.33 revs/sec

3.33 revs/sec = 6.66(pi)rads - - - answer?

**Fermat** · Nov30-05, 04:28 PM

Yes, that's right.

**suspenc3** · Nov30-05, 04:42 PM

ok..and is angular speed measure in revs/sec or rad/sec

Also..another part asks

What constant angular acceleration (in rev/min^2) will increase the wheels angular speed to 100 rev/min in 60 seconds?

I used:

$LaTeX Code: \\alpha = \\frac{\\Delta \\omega}{ \\Delta t}$

1000 revs/min = [2000(pi)revs/min - 400(pi)revs/min] / 1(minute)

$LaTeX Code: \\alpha = 1600 \\frac{revs}{min^2}$

**suspenc3** · Nov30-05, 04:46 PM

and it also asks how many rotations did this take could I just assume since its a constant acceleration that i took 1600 revs?

**Fermat** · Nov30-05, 05:00 PM

Angular speed is usually given in rads/sec, but, depending upon the application, it can also be measured in rpm or cps, for example.

alpha = 1600 revs/min² is correct.
But you have changed the initial angular velocity from 200 rev/min to 2000 rev/min.
Is this a typo, or a different situation with a different speed.

To find the number of rotations. You are being asked to find the (angular) distance travelled.
Do you remember this,

v² - u² = 2as ??

What do you think is its equivalent in circular motion ?

Use that.

**suspenc3** · Nov30-05, 05:06 PM

its suppose to be increased to 1000 rpm

isnt it $LaTeX Code: \\omega_f - \\omega_i$

**suspenc3** · Nov30-05, 05:11 PM

What do the variables stand for...i.e - u, a, s, v?

**Fermat** · Nov30-05, 05:15 PM

u = initial (linear) speed
v = final (linear) speed
a = (linear) acceleration
s = (linear) distance travelled

Can you now transpose that (linear) eqn into its circular/rotational equivalent ?

**suspenc3** · Nov30-05, 05:20 PM

so:

$LaTeX Code: \\frac{ \\Delta \\omega}{2 \\alpha} = d$

**Fermat** · Nov30-05, 05:27 PM

Almost there, but not quite :(

$LaTeX Code: \\mbox{linear: } v^2 - u^2 = 2as$
$LaTeX Code: \\mbox{circular: } \\omega _f^2 - \\omega _i^2 = 2\\alpha\\theta$

$LaTeX Code: \\omega _f^2$ is the final angular velocity
$LaTeX Code: \\omega _i^2$ is the initial angular velocity
$LaTeX Code: \\alpha$ is the angular acceleration
$LaTeX Code: \\theta$ is the rotational displacement

**suspenc3** · Nov30-05, 05:38 PM

Ok so (2000^2 - 400^2)/2(1600) = $LaTeX Code: \\theta$

= 1200

circumferance of wheel = 2(pi)r = 3.77m

1200m/3.77m = 318revs?

**Fermat** · Nov30-05, 05:42 PM

You are working in revs/min and revs/min² for velocity and acceleration so your displacement (theta) will be in revs.

i.e. theta = 1200 revs (rotations)