Angular Velocity of Disk After Bullet Impact: Calculation Explanation

[khurram usman]

A disk of radius R and mass M is mounted with its axis vertical.It is inially at rest.A bullet of mass m and velocity v is fired horzentally and tengential to disk .It enters the disc at its perimeter.What angular velocity will be acquired by disk?
1=mv/(m+M)R
2=mv/(2M+m)R
3=Mv/mR
4=2mv/(MR+2mR)
5=(m+2M)v/MR

please explain how u compute the answer

 

[cepheid]

Have you considered applying the conservation of angular momentum?

Hint: what is the angular momentum of the bullet around the disc's centre just prior to impact? What is the angular momentum due to the combined rotation of the disc+bullet around the disc's centre after the collision?

 

[khurram usman]

Have you considered applying the conservation of angular momentum?

Hint: what is the angular momentum of the bullet around the disc's centre just prior to impact? What is the angular momentum due to the combined rotation of the disc+bullet around the disc's centre after the collision?

ok...i see the approach
the angular momentum of bullet at tangent to disk will be mvR
now how to calculate velocity?

 

[Doc Al]

the angular momentum of bullet at tangent to disk will be mvR

Good.

now how to calculate velocity?

First answer cepheid's second question.

 

[khurram usman]

Good.

First answer cepheid's second question.

well as i see it the combined angular momentum after collision will be (m+M)Rv'
correct??

 

[Doc Al]

well as i see it the combined angular momentum after collision will be (m+M)Rv'
correct??

No, not quite. How would you express the angular momentum of a rotating disk? How does the presence of the bullet stuck onto the disk change that?

 

[khurram usman]

No, not quite. How would you express the angular momentum of a rotating disk? How does the presence of the bullet stuck onto the disk change that?

maybe the bullet changes mass distibution
i am not quite getting it

 

[Doc Al]

maybe the bullet changes mass distibution

Sure it does.

But before worrying about disk + bullet, how would you express the angular momentum of a rotating disk alone?