# Angular Momentum of a Uniform Rod

• Bob4321
In summary, the conversation was about a homework problem involving a uniform rod and a particle of unknown mass attached to it by a string. The goal was to find the mass of the particle and the amount of energy dissipated during a collision. The conversation included attempts at a solution and clarification on the equations being used. The expert advised against blindly plugging in numbers and suggested understanding the concepts behind the equations. They also pointed out an error in the attempted solution and provided guidance for solving the problem correctly.
Bob4321
<< Mentors have notified the OP to show their Attempt at a Solution >>

1. Homework Statement

A uniform rod of length L1 = 1.5 m and mass M = 2.8 kg is supported by a hinge at one end and is free to rotate in the vertical plane. The rod is released from rest in the position shown. A particle of mass m is supported by a thin string of length L2 = 1.1 m from the hinge. The particle sticks to the rod on contact. After the collision, θmax= 45°.

a)Find m (in kg)

b) How much energy is dissipated during the collision? (in J)

## Homework Equations

I found the question with different numbers but when I plug in mine. It's still wrong.

## The Attempt at a Solution

Last edited by a moderator:
Bob4321 said:

## Homework Statement

A uniform rod of length L1 = 1.5 m and mass M = 2.8 kg is supported by a hinge at one end and is free to rotate in the vertical plane. The rod is released from rest in the position shown. A particle of mass m is supported by a thin string of length L2 = 1.1 m from the hinge. The particle sticks to the rod on contact. After the collision, θmax= 45°.

a)Find m (in kg)

b) How much energy is dissipated during the collision? (in J)

## Homework Equations

I found the question with different numbers but when I plug in mine. It's still wrong.
View attachment 85506

View attachment 85501 View attachment 85502 View attachment 85503 View attachment 85504 View attachment 85505

## The Attempt at a Solution

Hello Bob4321. Welcome to PF.

Please show your attempt. What did you do in attempting to use that solution?

Solution Attempt:

Ok so for A:

ω1=((1/3)(2.8)(1.52))/ ((1/3)(2.8)(1.52))+m(1.12)√3(9.81m/s2)/1.5= (4.429kg/s)/(2.1kg)+1.21m

½(4.429kg/s)2/(2.1kg)+1.21m I don't know what to do now. Where did they get the .2 from in their example?

Last edited:
Bob4321 said:
Solution Attempt:

Ok so for A:

ω1=((1/3)(2.8)(1.52))/ ((1/3)(2.8)(1.52))+m(1.12)√3(9.81m/s2)/1.5= (4.429kg/s)/(2.1kg)+1.21m

½(4.429kg/s)2/(2.1kg)+1.21m I don't know what to do now. Where did they get the .2 from in their example?
What is (½)(1 - cos(θmax) ) ?

It looks like you have an issue regarding "order of operations". The entire expression, (⅓)(2.8)(1.52)+m(1.12) should be in the denominator. It's clear that in the solution you're attempting to mimic, the mass, m, is in the denominator.In my opinion: This method of obtaining an answer for an exercise is not to be recommended. If you don't know what quantities are being used, and why they're used, simply getting an answer to work out numerically isn't of much use.

Examining a worked out solution can indeed be very helpful, but don't just try to plug in some numbers into something that you don't understand.

Ok I have figured out that the .2 is from 1-cos but I still keep getting the wrong answer! Could you solve it so I can see what you did?

Last edited by a moderator:
For my problem the (1-cos45) is .48

Bob4321 said:
Ok I have figured out that the .2 is from 1-cos but I still keep getting the wrong answer! Could u solve it so I can see what you did?
That's not how we do things here at PF.

0.48 Is incorrect. Were you using 45 radians rather than 45° ?

## 1. What is Angular Momentum?

Angular momentum is a measure of how much rotational motion an object has and is defined as the product of the moment of inertia and the angular velocity of the object.

## 2. How is Angular Momentum of a Uniform Rod Calculated?

The Angular Momentum of a Uniform Rod can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

## 3. What is a Uniform Rod?

A Uniform Rod is a rigid object with a uniform mass distribution along its length, meaning that each section of the rod has the same mass per unit length.

## 4. How does the Length of a Uniform Rod Affect its Angular Momentum?

The length of a Uniform Rod does not directly affect its angular momentum. However, the moment of inertia, which is a factor in calculating angular momentum, does depend on the length of the rod. A longer rod will have a larger moment of inertia and thus a greater angular momentum.

## 5. What is the Conservation of Angular Momentum?

The Conservation of Angular Momentum states that in the absence of external torques, the total angular momentum of a system remains constant. This means that the angular momentum of a Uniform Rod will remain constant if no external forces act upon it.

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