Finding angular speed given T and I

[lespiderboris]

Homework Statement

A constant torque of 25.5 N · m is applied to a grindstone whose moment of inertia is
0.117 kg · m2.
Using energy principles, and neglecting friction, find the angular speed after the grind-
stone has made 14.6 rev.
Answer in units of rad/s

Homework Equations

1 rad = 1/2π rev (π = pi)

T=Iα (α = alpha = angular acceleration)(T=torque)

α=Δω/t

The Attempt at a Solution

All I've got it that 14.6 rev = 91.7345...rad.
... I think those are the only relevant equations since we don't know the radius or the mass OR the initial velocity of the grindstone. (Do we assume it was at rest? Does it even matter?) I must be wrong though as I am stumped on how to solve this. Thank you to anyone able and kind enough to help!

 

[nasu]

The text indicate that you are expected to use "energy principles".
Do you know the work-energy theorem?
And yes, you can assume it starts from rest.

 

[lespiderboris]

I know I₁ω₁=I₂ω₂

And that the total angular momentum of a system is conserved, i.e. remains constant.

Is that where you're leading me? :)

 

[nasu]

These are angular momenta and not energies.
And you have torque so the angular momentum is not conserved.
No, the work-energy theorem states that the change in kinetic energy is equal to the work done by the external force. In this case, taking the initial KE =0, you will have final KE=work.
You will have to express this in angular quantities and solve to find the angular velocity.