I am slipping off my spinning disc-

[Toododd]

I am slipping off my spinning disc--

Homework Statement

I am taking a non calculus based physics class and have hit a wall with this one. I have a horizontal spinning disc with an Angular Acceleration of .25 rad/s^2 from rest. The disc has a radius of .05 m. A pebble is placed .025m from the center point of the disc and it has a coeff.of static friction of .15. How long will it take for the pebble to slip off the disc? And how many revolutions will the disc have rotated through that time?

Homework Equations

Wi=Wf + alpha T. But since I can't get T or W I am stuck. If they had furnished a time or rpms or any other bones I could have gotten it.

The Attempt at a Solution

I think centripetal acceleration is the key but again without any W I am stuck.
Help please.

 

[Kurdt]

Homework Statement

I am taking a non calculus based physics class and have hit a wall with this one. I have a horizontal spinning disc with an Angular Acceleration of .25 rad/s^2 from rest. The disc has a radius of .05 m. A pebble is placed .025m from the center point of the disc and it has a coeff.of static friction of .15. How long will it take for the pebble to slip off the disc? And how many revolutions will the disc have rotated through that time?

Homework Equations

Wi=Wf + alpha T. But since I can't get T or W I am stuck. If they had furnished a time or rpms or any other bones I could have gotten it.

The Attempt at a Solution

I think centripetal acceleration is the key but again without any W I am stuck.
Help please.

The highlighted part of the question should give you a clue as to what the initial angular velocity is. Be careful with the equation you've posted since its not correct.

Centrifugal force is key to the problem. You will have to find the max. force the pebble can withstand before slipping and find what angular speed will produce that centrifugal force using equations of circular motion.

 

[Toododd]

Here is the correct formula-- It was late and I am really stressed by this stuff.
Wf=Wi + alphaT.
I have 10 formulas in front of me and I have plugged in the known factors into all of them including using initial angular acceleration of 0 and final angular acceleration of .25rad/s^2.
I have read that the centripetal force equals the friction force so I blindly put it the Fc=(mv^2)/r. Even though I knew it would not work to give me velocity.
I think I am lacking a complete understanding of how the system works as a whole.
BTW my tutor has given up on this too.

 

[Kurret]

Shouldnt the question be the time until the pebble starts slipping? there is actually a time fom when it starts slipping until it goes off the disc, and i think calculating that time requires calculus. (which is an interesting problem though)

 

[Kurdt]

Really its a fairly simple problem. So what is frictional force given by? If you substitute that for F_c in the equation you have above, can you solve for velocity then?

Edit: Thats a good spot Kurret that is what I had assumed originally.

 

[Toododd]

Here is the exact problem:
A horizontal disc of radius 5.00cm accelerates angularly from rest with an angular acceleration of .250 rad/s. A small pebble located halfway out from the center has a coefficient of static friction with the disc of 0.15. A. How long will the pebble take to slip on the disk surface? B.How many revolutions will the disc have rotated through that time?

If I substiture 0.15 for Fc I get 0.15 = (m * V^2)/.025.
I have no mass or velocity so I can't get either and even if I did I don't know what I would do with it.

 

[Kurdt]

Frictional force is not just given by the coefficient of friction. Have a look at the following.

http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html