- #1
zoom1
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Didn't get this equation which is written for the pendulum part of the cart.
Must be easy but couldn't get it.
Understanding the Pendulum Dynamics Equation for a Cart
- Thread starter zoom1
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Homework Help Overview
The discussion revolves around understanding the dynamics of a pendulum attached to a cart, specifically focusing on the equation governing the pendulum's motion. Participants are attempting to clarify the components of the equation and their physical implications.
Discussion Character
- Conceptual clarification, Mathematical reasoning
Approaches and Questions Raised
- Participants are exploring the relationship between force, mass, and acceleration in the context of the pendulum's motion. Questions arise regarding the interpretation of the centripetal force component and its role in the equation.
Discussion Status
Some participants have provided insights into the terms of the equation, such as tangential and radial accelerations, while others express confusion about specific components, particularly the centripetal force. The discussion is ongoing, with various interpretations being explored.
Contextual Notes
There is mention of a diagram that lacks clarity regarding the length of the rod, which may affect the understanding of the equation. Participants are also navigating the implications of the terms used in the equation without reaching a definitive conclusion.
Didn't get this equation which is written for the pendulum part of the cart.
Must be easy but couldn't get it.
- #2
AlephZero
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It is just "force = mass x acceleration" in the x direction, for the center of mass of the rod. (The length of rod isn't shown on your diagram, but if the equation is correct it is 2l, not l).
The ##\ddot\theta## term is from the tangential acceleration of the rod.
The ##\dot\theta^2## term is the from the radial (centripetal) acceleration.
The ##\ddot\theta## term is from the tangential acceleration of the rod.
The ##\dot\theta^2## term is the from the radial (centripetal) acceleration.
- #3
zoom1
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AlephZero said:
It's a little clearer now, but didn't understand the centripetal force component.
Isn't it
- #4
AlephZero
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Yes.
You also know ##v = \omega r## and ##\omega = \dot\theta##
The centripetal force is radial (along the length of the rod), but the equation is for the component of the force in the X direction.
You also know ##v = \omega r## and ##\omega = \dot\theta##
The centripetal force is radial (along the length of the rod), but the equation is for the component of the force in the X direction.