Angular velocity find angular displacement

[tachu101]

Homework Statement

A body with moment of inertia 20kgm^2 is rotating about a fixed axis with an angular velocity of w(t)= 3t^2-4

a. Through what angular displacement will the body move in the first 3 seconds
b. What is the new torque exerted on the object at t=2

Homework Equations

Angular Kinematics equations

The Attempt at a Solution

I integrated the angular velocity to get the displacement to be Theta(t)=t^3-4t ... then I evaluated the definite integral from 0 to 3 to get 15. But 15 What? Am I doing this right?

I don't know what to do for the second part. Does anyone know?

 

[rootX]

b) What's angular acceleration and torque formula?

 

[tachu101]

torque = Ia so it would then be derivative of w(t)= 3t^2-4 to get 6t evaluated at 2 gets 12. Then you do 12 times 20 to get 240?

 

[tachu101]

Does any of this look good?

 

[tachu101]

Anyone?

 

[radou]

Looks good to me.

 

[tiny-tim]

A body with moment of inertia 20kgm^2 is rotating about a fixed axis with an angular velocity of w(t)= 3t^2-4

a. Through what angular displacement will the body move in the first 3 seconds
b. What is the new torque exerted on the object at t=2
…
I integrated the angular velocity to get the displacement to be Theta(t)=t^3-4t ... then I evaluated the definite integral from 0 to 3 to get 15. But 15 What? Am I doing this right?

Hi tachu101!

(have an omega: ω and a theta: θ )

Yes, that's fine … and the 15 has no dimensions … it's just an angle (in degrees or radians, depending on what w is, so you needn't say).

torque = Ia so it would then be derivative of w(t)= 3t^2-4 to get 6t evaluated at 2 gets 12. Then you do 12 times 20 to get 240?

Also fine (though you could have stated it a little more logically )