Which point to sum the moments?

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SUMMARY

The discussion centers on the confusion regarding the summation of moments in a physics problem involving a crate's motion. The user initially attempted to sum moments about points C and D, concluding that both normal forces are 0.5mg, which was incorrect. The correct approach involves summing moments about point G, as this method accounts for the crate's mass center accelerating to maintain centripetal motion, which is essential for solving the problem accurately. The user highlights the importance of including the terms ma_{x} and ma_{y} in the moment equation for a comprehensive analysis.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of centripetal motion
  • Knowledge of moment calculations in physics
  • Basic algebra for solving equations
NEXT STEPS
  • Study the principles of summing moments in static and dynamic systems
  • Learn about centripetal acceleration and its effects on forces
  • Explore advanced problem-solving techniques in mechanics
  • Review examples of moment equations in physics textbooks
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for clarification on teaching moment calculations.

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Homework Statement


Here is the problem:
ttiFC.png


Here is the solution:
nO01d.png


I am confused about part c.


The Attempt at a Solution


Here is my attempt at part c:
vfZNS.png


I don't get why the answer key solution sums the moments about point G. I decided to sum up the moments about C and D and found out both normal forces are 0.5mg. However I quickly find out this is wrong because I am unable to solve the rest of the problem (which I did not include).
 
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If you take moments about D, say, you should not get a zero result. The crate's mass centre is accelerating to maintain its centripetal motion. This requires a moment about D. Taking moments about G avoids this.
 
What about ma_{x} and ma_{y} in your moment equation?

P.S. Sorry haruspex, I didn't see you already replied.
 

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