Finding the Axis of Rotation with Given CoG and Force Point

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SUMMARY

The discussion focuses on determining the axis of rotation for a square body given its center of gravity and a point of external force application. The center of gravity is identified as the geometric center of the square, while the external force acts at the bottom right corner. The key conclusion is that the axis of rotation passes through a point where the net torque from both gravity and the external force is zero. The participant struggles with the resulting equations, which yield multiple solutions, indicating a misunderstanding of the problem's constraints.

PREREQUISITES
  • Understanding of torque and its calculation in physics.
  • Familiarity with the concepts of center of mass and center of gravity.
  • Basic knowledge of Newton's Second Laws of motion.
  • Ability to interpret and manipulate equations involving trigonometric functions.
NEXT STEPS
  • Study the principles of torque equilibrium in rigid body dynamics.
  • Learn about the mathematical formulation of Newton's Second Laws for rotational motion.
  • Explore the concept of Fresnel Integrals and their applications in physics.
  • Investigate methods for solving systems of equations with multiple variables in physics problems.
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Students and professionals in physics, mechanical engineering, and robotics who are involved in analyzing rotational dynamics and torque applications.

  • #31
pointdexter16 said:
Ok
Turns out I was a little hasty of suggesting to find a closed form for ##x(t)## and ##y(t)##. You can write the equations down, but I think it results in some non-elementary integrals involving ##\sin \left( kt^2 \right)##, and ##\cos \left( kt^2 \right)##...

See: Fresnal Integral
 
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  • #32
erobz said:
Turns out I was a little hasty of suggesting to find a closed form for ##x(t)## and ##y(t)##. You can write the equations down, but I think it results in some non-elementary integrals involving ##\sin \left( kt^2 \right)##, and ##\cos \left( kt^2 \right)##...

See: Fresnal Integral
If possible could you provide me with the whole solution
 
  • #33
pointdexter16 said:
If possible could you provide me with the whole solution
Sorry, No. I can't. But you can write down Newtons Second Laws for the is object and figure out what I'm talking about. Afterword, if you are still curious then take it to the Mathematicians in here to see what they can do with it.
 

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