## [SOLVED] Angular speed problem

1. The problem statement, all variables and given/known data
A cylinder with mass m1 = 4.00kg, and radius 30cm, rotates about a vertical, frictionless axle with angular velocity of 8.00 rev/s. A second cylinder, this one have a mass of m2 = 3.00kg, and radius 20cm, initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular speed.
A) calculate the final angular speed
B)Find the energy lost in the system due to the interaction of the two cylinders.

3. The attempt at a solution
Just wondering if this is right:

I converted the 8 rev/s to 50.265 rad/s. I wasn't sure if i needed to but I did it anyway.

$$L_{i} = L_{f}$$
$$I_{1}\omega_{1i}^2 = (I_{1} + I_{2})\omega_{f}^2$$
$$\omega_{f} = \sqrt{\frac{I_{1}\omega_{1i}^2}{(I_{1} + I_{2})}}$$
$$= \sqrt{\frac{(.5)(4)(0.3^2)(50.265^2)}{(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)}$$

Then for part B, I found the loss of energy due to friction using the change in kinetic energy.

$$0.5(I_{1} + I_{2})\omega_{f}^2 - 0.5(I_{1})\omega_{f}^2^2$$
$$0.5[(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)](43.53)^2 - 0.5((.5)(4)(0.3^2)(50.265)^2$$

= 51.17 J

Did I solve this problem correctly?
 Recognitions: Gold Member Homework Help Angular momentum is $$L = I\omega$$. $$\omega$$ is NOT squared.
 crap. Other then that is that the right process (don't mind the numbers now)

Recognitions:
Gold Member
Homework Help

## [SOLVED] Angular speed problem

Yes, I think your approach is OK.
The text passage contains a physics problem involving angular speed and the interaction between two cylinders. The problem is broken down into two parts: calculating the final angular speed and finding the energy lost in the system. The author provides their attempt at solving the problem and asks for verification.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## [SOLVED] Angular speed problem

1. The problem statement, all variables and given/known data
A cylinder with mass m1 = 4.00kg, and radius 30cm, rotates about a vertical, frictionless axle with angular velocity of 8.00 rev/s. A second cylinder, this one have a mass of m2 = 3.00kg, and radius 20cm, initially not rotating, drops onto the first cylinder. Because of friction between the surfaces, the two eventually reach the same angular speed.
A) calculate the final angular speed
B)Find the energy lost in the system due to the interaction of the two cylinders.

3. The attempt at a solution
Just wondering if this is right:

I converted the 8 rev/s to 50.265 rad/s. I wasn't sure if i needed to but I did it anyway.

$$L_{i} = L_{f}$$
$$I_{1}\omega_{1i}^2 = (I_{1} + I_{2})\omega_{f}^2$$
$$\omega_{f} = \sqrt{\frac{I_{1}\omega_{1i}^2}{(I_{1} + I_{2})}}$$
$$= \sqrt{\frac{(.5)(4)(0.3^2)(50.265^2)}{(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)}$$

Then for part B, I found the loss of energy due to friction using the change in kinetic energy.

$$0.5(I_{1} + I_{2})\omega_{f}^2 - 0.5(I_{1})\omega_{f}^2^2$$
$$0.5[(0.5)(4)(0.3^2) + (0.5)(3)(0.2^2)](43.53)^2 - 0.5((.5)(4)(0.3^2)(50.265)^2$$

= 51.17 J

Did I solve this problem correctly?
 Recognitions: Gold Member Homework Help Angular momentum is $$L = I\omega$$. $$\omega$$ is NOT squared.
 crap. Other then that is that the right process (don't mind the numbers now)

Recognitions:
Gold Member
Homework Help

## [SOLVED] Angular speed problem

Yes, I think your approach is OK.
user
The text passage contains a physics problem involving angular speed and the interaction between two cylinders. The problem is broken down into two parts: calculating the final angular speed and finding the energy lost in the system. The author provides their attempt at solving the problem and asks for verification.

TYPE: SINGLE_QUESTION_WITH_ANSWER