# Simple Energy Equation for Pendulum (1 Viewer)

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#### joe_23

1. The problem statement, all variables and given/known data

Solve for the equation of motion of a simple pendulum using energy methods assuming it is a massless rod with a point mass at the end

2. Relevant equations

Translational Kinetic Energy T = 1/2mv^2

m is mass and v is linear velocity

Rotational Kinetic Energy T = 1/2Iw^2

I = mr^2

I is inertia, and w is angular velocity, r is mass radius
3. The attempt at a solution
I've read many times that the total kinetic energy of a mechanical system is a combination of the translational energy and the rotational energy. If my understanding is correct, then taking your mouse cursor and moving it in a circle would be only translational motion since the cursor's orientation is always the same relative to an inertial RF (it is upright at all times). For a pendulum, the mass at the end would rotate with the rod (its not upright at all times- instead it tilts from one side to the other), and therefore has rotational motion in addition to the linear motion of the path of its CM . Is there something wrong in my logic? Using newtons or eulers method gives you the same result as omitting the rotational kinetic energy term (or linear since theyre equal) so I would like to know why my logic is not correct.

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#### joe_23

This question comes from pretty much all physics textbooks; is the answer that they model the mass at the end as being very small so that I is zero and can be ignored?

#### Redbelly98

Staff Emeritus
Homework Helper
Welcome to Physics Forums!
This question comes from pretty much all physics textbooks; is the answer that they model the mass at the end as being very small so that I is zero and can be ignored?
Yes. Point masses have zero moment of inertia, so the kinetic energy is completely due to translational motion.

Don't forget about the potential energy.

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