What Is the Angular Velocity of a Spinning Disk?

[SalsaOnMyTaco]

Homework Statement

Ive been working on this two last questions and I can't seem to get the right set up.

A disk with a diameter of 0.04 m is spinning with a constant velocity about an axle perpendicular to the disk and running through its center.

-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)?
13.19 rev/s

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?
.828 m/s

At this same frequency, what is the period of rotation of this "halfway point"?

How long does it take a point on the edge of the disk to travel 1 km?

Homework Equations

Period (time)
T= 2∏/ω

Centripetal Acceleration
α=rω²

The Attempt at a Solution

First, I try to find the angular velocity at the halfwaypoint
14(9.81)=.01w² ω=117.19 rad/s

then i punch in
T=2∏/117.19 rad/s T=.053 sec?

Once i typed in the answer, it says is wrong

 

[SalsaOnMyTaco]

woah okay no, should i find the frequency and then divide 1/f ?

 

[tiny-tim]

Hi SalsaOnMyTaco!

First, I try to find the angular velocity at the halfwaypoint …

Why would the angular velocity be any different?

 

[TSny]

Why did you use .01 m for r? Note that it's 14 g's at the outer edge.

 

[SalsaOnMyTaco]

Hi SalsaOnMyTaco!


Why would the angular velocity be any different?

isnt velocity different on a different part of the radius

Why did you use .01 m for r? Note that it's 14 g's at the outer edge.

The total diameter of the disk is .04, radius is .02, half way of the radius is .01

 

[TSny]

But the problem states that the acceleration is 14 g's for a point on the outer edge of the disk (r = 0.02 m), not at a halfway point (r = 0.01 m).

 

[tiny-tim]

Why would the angular velocity be any different?

isnt velocity different on a different part of the radius

ahh!

you're confusing angular velocity with tangential velocity (ie component of velocity along the "angular" unit vector $\boldsymbol{\hat{\theta}}$)

angular velocity is angle per second, dθ/dt, it's not a velocity at all