# Angular Momentum problem, Swinging door

• sreya
In summary, the problem involves a solid wood door being struck by a handful of sticky mud, causing it to rotate. Using the conservation of angular momentum equation, we can determine the final angular speed of the door. To do this, we must calculate the moment of inertia for both the door and the mud, which can be found in a textbook. The mud can be treated as a point particle for calculation purposes.
sreya

## Homework Statement

A solid wood door 1.00 m wide and 2.00 m high is hinged along one side and has a total mass of 42.0kg . Initially open and at rest, the door is struck at its center by a handful of sticky mud with mass 0.400kg , traveling perpendicular to the door at 11.0m/s just before impact.

Find the final angular speed of the door.

## Homework Equations

Conservation of angular momentum

$rmvsin\theta=l$

## The Attempt at a Solution

$L_{mud}=L_{door\&mud}$

$rmvsin\theta=(I_{door}+I_{mud})\omega$

$.5(.5)(14)sin(90^o)=(I_{door}+I_{mud})\omega$

How do I determine the inertias for the mud and the door??

## 1. What is the Angular Momentum Problem in relation to a Swinging Door?

The Angular Momentum Problem in a Swinging Door refers to the difficulty in predicting the exact path and behavior of a swinging door when it is in motion. This is due to the fact that the door's angular momentum, which is a measure of its rotational motion, constantly changes as it swings open or closed.

## 2. How is Angular Momentum related to a Swinging Door?

Angular Momentum is related to a Swinging Door because it is a measure of the door's rotational motion. As the door swings, its angular momentum changes, making it difficult to accurately predict its behavior.

## 3. What factors affect the Angular Momentum of a Swinging Door?

The Angular Momentum of a Swinging Door is affected by a number of factors, such as the mass of the door, the speed at which it is swung, and the distance of the door from its pivot point. These factors all contribute to the door's angular momentum, which determines its behavior.

## 4. How do you calculate the Angular Momentum of a Swinging Door?

The Angular Momentum of a Swinging Door can be calculated using the equation L = Iω, where L is the angular momentum, I is the moment of inertia (a measure of the door's resistance to rotational motion), and ω is the angular velocity (the rate at which the door is rotating).

## 5. What are some real-world applications of the Angular Momentum Problem in a Swinging Door?

The Angular Momentum Problem in a Swinging Door has several real-world applications, such as in the design of revolving doors, wind turbines, and even sports equipment like golf clubs and baseball bats. Understanding the principles of angular momentum can help engineers and designers create more efficient and stable structures and objects.

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