Kinematics of Inverted Physical Pendulum

In summary, the conversation discusses finding the angular velocity of a pivoted stick as it hits a table. The suggested solution involves using the parallel axis theorem and conserving mechanical energy. It is noted that the stick does not have translational kinetic energy as it is not rolling.
  • #1
HoloBarre
7
0

Homework Statement



A stick of mass M, length L, stands upright on a table, pivoted to the table.

What is the angular velocity as it hits the table?


Homework Equations



ang. accel = (3g/2L)cos theta

w = (3g/2L) integral cos theta dt


The Attempt at a Solution



theta (t) = ?

Solution involves elliptic integrals?? Not familiar with numeric methods.

Any approximation of the velocity at the table would be good for now.
 
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  • #2
Why don't you conserve mechanical energy?
 
  • #3
aim1732 said:
Why don't you conserve mechanical energy?

Yeah this seems right. All you need to use is the parallel axis theorem, find the initial potential energy and solve for omega noting that the stick gains both rotational and translational kinetic energy.
 
  • #4
Translational?
 
  • #5
linear kinetic energy 1/2mv2 instead of 1/2Iw2

Actually thinking about it, it's not rolling so there probably wouldn't be translational kinetic energy gained.
 

Related to Kinematics of Inverted Physical Pendulum

1. What is a physical pendulum?

A physical pendulum is a type of pendulum that consists of a rigid body suspended from a pivot point and allowed to swing freely. Unlike a simple pendulum, which is a point mass suspended from a string, a physical pendulum has a mass and size that affect its motion.

2. What is an inverted physical pendulum?

An inverted physical pendulum is a pendulum with its pivot point located above its center of mass. This means that when the pendulum is released, it will swing in an inverted or upside-down motion instead of a traditional back-and-forth motion.

3. What is the significance of studying the kinematics of inverted physical pendulums?

Studying the kinematics of inverted physical pendulums allows us to better understand the principles of motion and energy conservation. It also has practical applications in fields such as robotics, where inverted pendulums can be used as a control system for balancing and stabilization.

4. How is the motion of an inverted physical pendulum described?

The motion of an inverted physical pendulum is described using the equations of motion for a rigid body, which take into account the pendulum's mass, length, and angle of displacement. These equations can be used to analyze the pendulum's motion and predict its behavior.

5. What factors affect the motion of an inverted physical pendulum?

The motion of an inverted physical pendulum is affected by factors such as its length, mass, angle of displacement, and the force of gravity. These factors can influence the pendulum's period, frequency, and amplitude of motion.

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