Torque v. Time Graph -- Find angular velocity

[adriannesmith]

Homework Statement

An object whose moment of inertia is 3.00kgm2experiences the torque shown in the figure (Figure 1) . What is the object's angular velocity at 2.80s ? Assume it starts from rest.
http://session.masteringphysics.com/problemAsset/1073771/4/knight_Figure_13_21.jpg

Homework Equations

Torque=angular acceleration * moment of inertia
angular velocity = angular acceleration * change in time

The Attempt at a Solution

From what I can understand of the problem, the angular acceleration is 0 (because torque is 0), but angular velocity is not zero so it must be some constant. However, I'm struggling how to figure out what that is.

 

[ehild]

The angular acceleration is the time derivative of angular velocity, so Idω/dt = τ. You get the angular velocity at a given instant by integrating the angular acceleration with respect to time.

 

[adriannesmith]

The angular acceleration is the time derivative of angular velocity, so Idω/dt = τ. You get the angular velocity at a given instant by integrating the angular acceleration with respect to time.

Could you please ellaborate in context of this problem? I just can't find any examples of problems like this so I just need a little bit more explanation

 

[adriannesmith]

By integrating angular acceleration with respect to time, I get w= at + c (constant). a= 0 t=2.8s but how do I determine the constant? Which will equal the velocity

 

[ehild]

By integrating angular acceleration with respect to time, I get w= at + c (constant). a= 0 t=2.8s but how do I determine the constant? Which will equal the velocity

Use definite integral.
$\frac{d\omega}{dt }= \frac {\tau (t)}{I}$. Integrate from t=0 to t=2.8 s. You have to do the integral separately in all the three time intervals and add them