Non-Uniform Circular Motion - Finding total acceleration

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SUMMARY

The discussion focuses on calculating total acceleration in non-uniform circular motion using the formula a(total) = sqrt(a(tangential)^2 + a(radial)^2). Participants derived the radial and tangential accelerations as a(radial) = (T/m) - (g * cos(θ)) and a(tangential) = g * sin(θ). A participant identified that further simplification using the identity sin^2(x) + cos^2(x) = 1 could yield a correct final expression. The conversation highlights common pitfalls in solving physics problems involving forces and accelerations.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Knowledge of trigonometric identities, specifically sin^2(x) + cos^2(x) = 1
  • Familiarity with circular motion concepts
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the derivation of centripetal acceleration in circular motion
  • Learn how to apply trigonometric identities in physics problems
  • Explore examples of non-uniform circular motion in real-world scenarios
  • Practice solving problems involving forces in radial and tangential directions
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators looking for problem-solving strategies in dynamics.

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Homework Statement



21jdoqu.jpg


Homework Equations


Code:
a(total) = sqrt( a(tangential)^2 + a(radial)^2 )

The Attempt at a Solution



I wrote out equations for the forces in the radial and tangential directions:
Code:
F(radial)       = T - ( mg * cos(θ) )
F(tangential) = mg * sin(θ)
I used the equations to find acceleration in the radial and tangential direction (a = F/m):
Code:
a(radial)       = (T/m) - ( g * cos(θ) )
a(tangential) = g * sin(θ)
I plugged it into a(total) = sqrt( a(tangential)^2 + a(radial)^2 ):
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which simplifies to:

4oCLY.gif


My answer is incorrect and I'm not sure what I did wrong.
Any help would be appreciated.
 
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is this some kind of online question bank where you have to submit the answer ?
i see that your solution seems to be correct... may be you need to further simplify the expression you got...these online physics problem banks can act stupid...

Newton
 
Your answer seems to be correct. I think you need to simplify the expression by using sin^2(x)+cos^2(x)=1. That may change the final expression, but otherwise, the answer is same.
 

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