Can Energy Conservation Solve the Angular Velocity Problem?

[nafisanazlee]

Homework Statement

A 10g small ball with negligible radius is moving with a constant velocity of 9m/s. there is a disk with center O that can move freely relative to the center. The small ball is moving in a line which has a perpendicular distance of 2m from the center O. Eventually the ball hits the disk and sticks to it. The disk has a mass of 40g and radius of 3m. What's the angular velocity of the disk after the collision?

Relevant Equations

Initial angular momentum= Final angular momentum

Let the mass of the ball m₁ and the disk m₂
m₁vrsinθ = I₁ω + Ι₂ω
I₁ = m₁r² and I₂ = ½m₂r², r=3m, rsinθ = 2m.
Is this a correct approach? if not, what is? Can this be solved using energy conservation?

 

[kuruman]

Angular momentum conservation is the correct approach. Energy conservation is not because the collision is perfectly inelastic. What angle is $\theta$? Please provide a diagram should you need additional help.

 

[nafisanazlee]

Angular momentum conservation is the correct approach. Energy conservation is not because the collision is perfectly inelastic. What angle is $\theta$? Please provide a diagram should you need additional help.

no theta is given, that's just the perpendicular distance 2m. Can you check if my solution is correct?

 

[kuruman]

no theta is given, that's just the perpendicular distance 2m. Can you check if my solution is correct?

Thank you for your diagram. I will be happy to check your solution when you provide it. The problem is asking you for the angular velocity of the disk after the collision. I don't see an equation in the form $\omega = \dots~~$ in what you have posted so far.

 

[nafisanazlee]

Thank you for your diagram. I will be happy to check your solution when you provide it. The problem is asking you for the angular velocity of the disk after the collision. I don't an equation in the form $\omega = \dots~~$ in what you have posted so far.

here's the solution I came up with

 

[kuruman]

That looks correct. If you plan to post here often, please use LaTeX for your equation. To learn how, click on "LaTeX Guide", lower left above "Attach files."

 

[nafisanazlee]

That looks correct. If you plan to post here often, please use LaTeX for your equation. To learn how, click on "LaTeX Guide", lower left above "Attach files."

Thanks so much!