Will a Meter Stick Rotate Around Its Center of Mass When Released?

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Homework Help Overview

The discussion revolves around the motion of a meter stick when released from a horizontal position and the dynamics of a mass projected along different paths. The original poster questions the point of rotation for the meter stick and explores the relationship between travel times for a mass moving along various tracks.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants consider the mechanics of rotation and the influence of gravity on the meter stick's motion. Questions arise about the conditions under which the stick rotates and the implications of its center of mass. Additionally, there is an inquiry into the effects of different track orientations on the travel times of a mass, with participants questioning which path allows for the fastest arrival at the endpoint.

Discussion Status

The discussion is active, with participants exploring the fundamental principles of motion and rotation. Some guidance has been offered regarding the initial question about the meter stick, while the second part regarding the mass on tracks has prompted further inquiry into the relationships between travel times.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for discussion. The original poster has provided a visual aid to support the second question, but the specifics of the tracks and conditions are not fully detailed.

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Very quick question: A uniform meter stick held by one end is swung in an arc and released when the person’s arm is horizontal, so that it moves initially away from the ground. About which point will it rotate as it flies before striking the ground?

Is it the 50cm mark since once released, the only force acting is gravity which acts at the centre of mass?

Thanks.
 
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Why would it rotate at all?
 
Whoops, you're right.

I have another question: A mass m starting at point A is projected with the same initial
horizontal velocity v0 along each of the three tracks shown here
(with negligible friction) sufficient in each case to allow the mass
to reach the end of the track at point B. (Path 1 is directed up,
path 2 is directed horizontal, and path 3 is directed down.) The
masses remain in contact with the tracks throughout their
motions. The displacement A to B is the same in each case, and
the total path length of path 1 and 3 are equal. If t1, t2, and t3 are
the total travel times between A and B for paths 1, 2, and 3,
respectively, what is the relation among these times?

Picture attached.

Does the ball in the straight track arrive faster? Why is that?
 

Attachments

These are the answer choices to the above question;

a) t3<t2<t1
b) t2<t3<t1
c) t2<t1=t3
d) t2=t3<t1
 

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