What is the Angular Velocity of a Falling Physical Pendulum?

In summary, a physical pendulum is a rigid body suspended from a fixed point that has a mass distribution and can have various shapes. It works by converting potential energy into kinetic energy and vice versa, and factors such as length, mass distribution, and initial angle of release can affect its motion. The period of a falling physical pendulum can be calculated using a specific formula. Real-life applications of physical pendulums include clocks, seismometers, accelerometers, and physics demonstrations and experiments.
  • #1
HoloBarre
7
0

Homework Statement



A stick of mass M, length L is standing upright on a table, pivoted at the bottom.
What is its angular velocity as it hits the table?



Homework Equations



ang. accel = (3g/2L)cos theta (theta is zero with stick laying on table)



The Attempt at a Solution



ang. vel = integral of ang. accel wrt to time, theta is some function of time.
Elliptic integral?

Numeric solution??

Thanks.
 
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  • #2
Use conservation of energy.

ehild
 

1. What is a physical pendulum?

A physical pendulum is a type of pendulum that consists of a rigid body suspended from a fixed point. Unlike a simple pendulum, which is a point mass suspended from a string, a physical pendulum has a mass distribution and can have various shapes, such as a rod or a disk.

2. How does a physical pendulum work?

A physical pendulum works by converting potential energy into kinetic energy and vice versa. When the pendulum is at its highest point, it has the most potential energy. As it swings downward, this potential energy is converted into kinetic energy, causing the pendulum to speed up. As it reaches the bottom of its swing, the kinetic energy is converted back into potential energy, causing the pendulum to slow down and swing back up.

3. What factors affect the motion of a falling physical pendulum?

The motion of a falling physical pendulum is affected by several factors, including the length of the pendulum, the mass distribution of the pendulum, and the initial angle of release. Other factors such as air resistance and friction can also have an impact on the motion of the pendulum.

4. How is the period of a falling physical pendulum calculated?

The period of a falling physical pendulum is calculated using the formula T = 2π * √(I/mgh), where T is the period, I is the moment of inertia of the pendulum, m is the mass of the pendulum, g is the acceleration due to gravity, and h is the distance from the pivot point to the center of mass of the pendulum.

5. What are some real-life applications of a physical pendulum?

Physical pendulums have a variety of real-life applications, including in clocks, seismometers, and accelerometers. They are also commonly used in physics demonstrations and experiments to study the laws of motion and conservation of energy.

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