Instantaneous Center: How to Solve Homework Equations

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Homework Help Overview

The discussion revolves around determining the angular velocity of a gear using the concept of the instantaneous center. Participants are exploring the application of relevant equations and methods in the context of rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various attempts to solve the problem using different equations, including the relationship between linear and angular velocities. Questions arise regarding the correct application of the instantaneous center method and the importance of sign conventions in calculations.

Discussion Status

The discussion includes attempts to clarify the use of the instantaneous center and the potential for calculation errors. Some participants suggest that issues may stem from sign mismanagement in the equations used. There is acknowledgment of the need for careful consideration of the methods employed.

Contextual Notes

Participants note the specific values given for linear velocities and the assumption that counterclockwise motion is positive. There is an indication of confusion regarding the application of methods and the conditions under which the instantaneous center should be used.

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Homework Statement


Determine the angular velocity of the gear at the instant shown. Set v = 9ft/s and vc = 6ft/s. Assume counterclockwise is positive.
LiUIPsu.png

Homework Equations


v = w x rIC

The Attempt at a Solution


I tried solving this many times using va = v0 + (ω x ra0 ) and vb=v0 + (ω x rb0 ) but kept getting the wrong answer.
Then I ended up solving for the instantaneous center using similar triangles and used v = ωxrIC.

How do I know when to use an instantaneous center in my problem solving?
 
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Nikstykal said:
I tried solving this many times using va = v0 + (ω x ra0 ) and vb=v0 + (ω x rb0 ) but kept getting the wrong answer.
Then the problem is somewhere in the steps you did not show.
Just a guess: Did you take the signs into account properly?
 
Nikstykal said:

Homework Statement


Determine the angular velocity of the gear at the instant shown. Set v = 9ft/s and vc = 6ft/s. Assume counterclockwise is positive.
LiUIPsu.png

Homework Equations


v = w x rIC

The Attempt at a Solution


I tried solving this many times using va = v0 + (ω x ra0 ) and vb=v0 + (ω x rb0 ) but kept getting the wrong answer.
Then I ended up solving for the instantaneous center using similar triangles and used v = ωxrIC.

How do I know when to use an instantaneous center in my problem solving?
Instantaneous centre method can be used in any problem.
But both methods give the same result. Maybe there's some problem with the signs like mfb said.
 
Thank you for helping! Sorry there was such a delay in my response. Yes it ended up being just a calculation error when mixing up the signs!
 

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