What is the initial acceleration of the rod's CM?

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Homework Help Overview

The problem involves a uniform rod of length 1.4 m, pivoted at one end and released from an angle of 23° above the horizontal. The focus is on determining the initial acceleration of the rod's center of mass (CM).

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the meaning of CM and the distinction between tangential and centripetal acceleration. Questions arise about the definitions and relationships between these types of acceleration.

Discussion Status

The discussion is ongoing, with participants clarifying concepts related to acceleration components and their dependencies. Some guidance has been provided regarding the definitions of tangential and centripetal acceleration, but no consensus has been reached on the initial acceleration specifics.

Contextual Notes

Participants are reviewing concepts in preparation for a test, indicating a focus on understanding rather than solving the problem directly. There is a noted uncertainty regarding the definitions and applications of different types of acceleration.

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Homework Statement


A uniform rod of length 1.4 m is attached to a frictionless pivot at one end. It is released from rest from an angle θ = 23° above the horizontal. Find the magnitude of the initial acceleration of the rod's CM.


Homework Equations


At = alpha * r


The Attempt at a Solution


I am reviewing old homework problems for my test tomorrow so I just have a few questions...
What is CM?
Also is At known as initial acceleration not Ac?
 
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CM stands for 'Centre of Mass' and since the rod is uniform one can work out the acceleration by looking at the net force acting on the rod's CM.
 
So is tangential acceleration known as initial acceleration not centripetal acceleration?
 
BuBbLeS01 said:
So is tangential acceleration known as initial acceleration not centripetal acceleration?
No, the tangential acceleration is orthogonal to the centripetal acceleration by definition.
 
In general, the acceleration of the center of mass (or any other point on the object) will have two components: centripetal and tangential. But what does the centripetal component depend upon?
 
centripetal depends on the forces acting on the object I think
 
BuBbLeS01 said:
centripetal depends on the forces acting on the object I think
Well, sure. But what I was going for was that centripetal acceleration depends on the speed of rotation. And immediately after this rod is released from rest, what is its initial rotational speed?
 
0 rad/s^2, I guess I am don't understand the difference between at and ac and when to use which one.
 
The tangential acceleration (which is proportional to the angular acceleration) has to do with the rate at which the angular speed changes. If the rate of rotation is constant, the tangential acceleration is zero.

But as long as the rod is rotating, the center of mass will have some centripetal acceleration.
 

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