Angular velocity find angular displacement

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Homework Help Overview

The problem involves a body with a moment of inertia rotating about a fixed axis, with a given angular velocity function. Participants are tasked with finding the angular displacement over a specified time interval and determining the torque at a specific moment.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to integrate the angular velocity function to find angular displacement and questions the meaning of the resulting value. There are inquiries about the formulas for angular acceleration and torque. Some participants discuss the relationship between torque and angular acceleration, suggesting a method for calculating torque based on the derivative of the angular velocity.

Discussion Status

Participants are actively engaging with the problem, providing feedback on each other's attempts. Some guidance has been offered regarding the interpretation of the angular displacement result and the calculation of torque, though there is no explicit consensus on the correctness of the approaches taken.

Contextual Notes

There is a mention of the need to clarify the units of the angular displacement result, as well as the logical flow in the explanation of torque calculations. Participants are navigating through the implications of their calculations without resolving the overall problem.

tachu101
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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?
 
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b) What's angular acceleration and torque formula?
 
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?
 
Does any of this look good?
 
Anyone?
 
Looks good to me.
 
tachu101 said:
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! :smile:

(have an omega: ω and a theta: θ :wink:)

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).
tachu101 said:
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 :wink:)
 

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