# Conservation of angular momentum

• Mohammeddev
In summary, the conversation discusses the angular velocity of a rod after a collision with a ball. By using the equation for conservation of angular momentum, the correct answer is found to be 7MvD/4I, where the 4 comes from a mistake in the initial calculations.
Mohammeddev

## Homework Statement

A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I

Li = Lf

## The Attempt at a Solution

the question is :
What is the angular velocity ω of the rod after the collision?
We know that the initial angular momentum is equal to the final angular momentum so i started with the ball because it's the only object in our system that has initial angular momentum:

MvD = -3MvD/4 + IW

doing some algebra:
MvD * 4 = -3MvD + IW
4MvD + 3MvD = IW
7MvD = IW
W = 7MvD/I

But the correct answer is :
7MvD/4I
my question where did the 4 come from ?
is my math Wrong ?

Mohammeddev said:
MvD = -3MvD/4 + IW

doing some algebra:
MvD * 4 = -3MvD + IW
Check what you are doing to go from the first equality to the second.
.

DrClaude said:
Check what you are doing to go from the first equality to the second.
.
Okay now i realized the mistake i made Thank you for making me recheck my answer i was so convinced that khan academy is wrong in this one !

## What is conservation of angular momentum?

Conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant in the absence of external torques.

## Why is conservation of angular momentum important?

Conservation of angular momentum is important because it helps us understand and predict the behavior of rotating systems, such as planets orbiting the sun or spinning tops.

## How is angular momentum conserved?

Angular momentum is conserved when the net torque acting on a system is zero. This means that the total amount of rotational energy in a system remains constant.

## What are some examples of conservation of angular momentum?

Some examples of conservation of angular momentum include the rotation of the Earth around its axis, the orbit of the Moon around the Earth, and the spinning of a figure skater as they pull their arms in.

## What happens if conservation of angular momentum is violated?

If conservation of angular momentum is violated, it means that there is an external torque acting on the system. This can result in changes in the rotational speed or direction of the system.

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