Disk with constant angular acceleration

[Bad Vibration]

Homework Statement

A disk is under constant angular acceleration [tex]\alpha[/tex]. When it starts from rest it takes 10 revolutions before it reaches angular velocity [tex]\omega[/tex]. How many additional revolutions does it take to accelerate the disk further to an angular velocity of 3[tex]\omega[/tex]?

The Attempt at a Solution

The answer is 80, I just can't figure out why.

 

[ashishsinghal]

Welcome to physics forum,
you first need to show your calculations and then i can help you solve the problem.
these are pf rules

 

[gneill]

Begin by writing the basic equations of rotational motion that you should know (they are analogs of the usual equations of linear motion). One should be for the rotational velocity given rotational acceleration and time, the other should be for angular distance given rotational acceleration and time.

 

[Bad Vibration]

Welcome to physics forum,
you first need to show your calculations and then i can help you solve the problem.
these are pf rules

Thank you! I actually don't have any calculations, I'm stuck. I tried writing the acceleration as:

[tex]\alpha[/tex] = [tex]\omega[/tex] / 10 per revolution

And then use

[tex]\theta[/tex] = 10 revs + [tex]\omega[/tex] *t +1/2 * [tex]\omega[/tex]/10 [tex]t^{2}[/tex]

t = (3[tex]\omega[/tex]-[tex]\omega[/tex]) / [tex]\omega[/tex]/10

But I just end up confusing myself, because having the angular acceleration increase with 1 tenth of an omega per revolution instead of radians per second squared. It is such a simple problem but I keep on leading myself down strange blind allies.

 

[gneill]

Best to ignore the numbers to begin with and work with the symbols. So, deal with the equations first. What are the equations you think you might need? You're dealing with rotational distance, rotational velocity, and rotational acceleration.