What Is the Kinetic Energy Equation for a Mass on a Double Pendulum?

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SUMMARY

The kinetic energy equation for a mass on a double pendulum can be expressed as K = 1/2 * I * ω², where I represents the moment of inertia and ω is the angular velocity. In the context of a double pendulum, the total angular velocity ω is the sum of the angular velocities of both bars. To determine the position of the mass or the angles of the bars at any given time, one must consider the torque τ(t) applied to the main bar. This discussion highlights the need for a solid understanding of dynamics and rotational motion principles.

PREREQUISITES
  • Understanding of Kinetic Energy and its equations
  • Familiarity with Torque and its application in dynamics
  • Knowledge of Angular Velocity and its calculation
  • Basic principles of Statics and Dynamics
NEXT STEPS
  • Research the concept of Moment of Inertia in rotational dynamics
  • Learn about the equations of motion for a double pendulum
  • Study the effects of torque on angular motion
  • Explore advanced dynamics topics, particularly in relation to oscillatory systems
USEFUL FOR

This discussion is beneficial for students in physics or engineering, particularly those studying dynamics, as well as hobbyists working on projects involving pendulum systems and rotational motion analysis.

Axecutioner
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You can treat the cable as another rigid bar in this case, both massless. I just need the equation for the Kinetic Energy of the mass on the end.

Is there an equation for if the main bar is torqued at a given τ(t), and any other necessary information is given, to find the position of the mass on the end or the angles of the two bars at any given time?

I'm in a Statics class right now and will be taking advanced dynamics in the fall but I'd like to work on a personal project in the fall. Done through Calc 4 and Stokes Theorem if it matters.

Thanks
 
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Burn the thread. The ball will remain and will perform free fall. Then you will easily get your answer.
 
That doesn't help at all.

I know K = 1/2*I*w^2 but what would the omega be? Just both angular velocities added together?
 
Sorry, misunderstanding. Please delete this post.
 
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