What is the Angular Acceleration of a Rod?

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Homework Help Overview

The discussion revolves around calculating the angular acceleration of a rod, involving concepts from rotational dynamics and torque. Participants are analyzing the relationships between torque, moment of inertia, and angular acceleration in the context of a physical setup involving a rod and gravitational forces.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate angular acceleration using a derived formula but encounters an incorrect result. Some participants question the application of the distance in the torque formula and suggest that the gravitational force should be considered at the center of mass rather than at the end of the rod. Others raise the need to account for the total mass of the system in the calculations.

Discussion Status

The discussion is ongoing, with participants providing guidance on the correct application of concepts. There is a focus on clarifying the assumptions regarding the point of force application and the total mass involved in the calculations. Multiple interpretations of the problem setup are being explored, but no consensus has been reached yet.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may impose specific methods or assumptions that are being questioned. The original poster's calculations and the assumptions about the rod's center of mass are under scrutiny.

euphtone06
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Homework Statement


http://img505.imageshack.us/img505/6741/rodprobbw3.gif"

Homework Equations


Itot= 1/3MrL^2 + 2/5 MsR^2 + Ms(L + R)^2 = 235.69784
Cm= (Mr(L/2) + Ms(L+r))/(Mr+Ms) = 4.915

angular accel = Torque/Itot
Torque= 1/2Lmgcos(theta)

The Attempt at a Solution


I solved for Itot and Center of mass and got the correct answers but, I am having a difficult time getting the angular acceleration correct.

Aa= .5Lmgcos(theta)/(Itot)
= .5*6*4*9.8cos31/235.697
= .42767 rad/s^2 which was incorrect
Please help don't know what went wrong!
 
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The 'L' in your angular acceleration formula should be the distance from the axis to the point where the force causing the torque is exerted. In this case the gravitational force can be treated as being exerted at the center of mass, not at the end of the rod.
 
Do you have to account for the total mass of the system?
.5*4.915*(4+4?)*9.8*cos31/235.697= .7 rad/s^2
 
4+4? Don't you mean 4+1? Yes, total mass of system. And it looks like the 1/2 in your torque equation is coming from the assumption that the center of mass is the center of mass of the rod. Get rid of it and just put L to be distance from axis to center of mass.
 

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