Torque v. Time Graph -- Find angular velocity

AI Thread Summary
To find the angular velocity of an object with a moment of inertia of 3.00 kgm² experiencing varying torque, the angular acceleration must be calculated from the torque using the equation τ = Iα. Since the torque is zero at certain intervals, the angular acceleration will also be zero, indicating that the angular velocity remains constant during those periods. The solution involves integrating the angular acceleration over time, which yields the angular velocity as a function of time. To determine the constant of integration, the initial condition (starting from rest) is applied, leading to the final angular velocity at 2.80 seconds. The integration must be performed over each time interval where torque is applied to accurately compute the total angular velocity.
adriannesmith
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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.
 
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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.
 
Last edited:
ehild said:
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
 
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
 
adriannesmith said:
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
 
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