# Spinning Disk (circular motion)

1. Feb 21, 2009

### Trentonx

1. The problem statement, all variables and given/known data
A disk with a diameter of 0.07 m is spinning about an axle perpendicular to the disk and running through its center.
a) How many revolutions per second would it have to rotate in order that the acceleration of the outer edge of the disk be 14 g's (i.e., 14 times the gravitational acceleration g)?
b) For the frequency determined in part (a), what is the speed of a point half way between the axis of rotation and the edge of the disk?
c) At this same frequency, what is the period of rotation of this "halfway point"?

2. Relevant equations
a_c=v$$^{2}$$/r
v=r $$\omega$$
a=r $$\alpha$$

3. The attempt at a solution
I tried substituting the angular velocity in the centripital acceleration, setting it equal to 14g
137.2=(rw)^2/r
w=44.27 rad/sec (I think), then dividing by 2pi for rev/sec.
That didn't work. So I'm stumped. our professor hasn't lectured on this at all, so I'm really lost on what to do.

2. Feb 21, 2009

### Delphi51

So you used a = (rw)^2/r = rw^2
or w = sqrt(a/r) ?
r = 0.035
It works out to 62.64 rad/sec or 9.97 revs/sec for me

3. Feb 21, 2009

### Trentonx

No, actually what I used was the diameter, not the radius. So now I have a and b, but what is a "period of rotation"? I know the speed at that point and the radius, so that's the circumference, should it be the speed divided by circumference?
V=1.09 m/s
r=.0175
C=.1099m

4. Feb 21, 2009

### Trentonx

I was making it too complicated. Just 1 over the frequency that we found. Thanks for your help.