Conservation of Angular Momentum

You have a ballistic pendulum. You shoot a ball of mass m horizontally from a spring gun with speed v. The ball is immediately caugt a distance r below a frictionless pviot by a pivoted cather assembly of mass M. the moment of inertia of this assembly about its rotation axis through the pivot is I. the distance r is much greater than the radius of the ball.

a) use conservation of angular momentum to show that the anguluar speed of the ball and catcher just after the ball is caught is w = mvr/(mr^2 + I)

b) after the ball is caught, the center of mass of the ball - catcher assembly system swings upp with the maximum height increase h. Use conservation of energy to show that w = sqrt[ 2(M + m)gh / (mr^2) + i) ].

c) your lab partner says that linear momentum is conserved in the collision and derives the expression mv = (m + M)V where V is the speed of the ball immediately after the collision, she then uses conservation of energy to derivate that V = sqrt(2gh), so that mv = (m + M)sqrt[2gh]. Use the results of parts (a) and (b) to show that this equation is satisfied only for the special case when r is given by I = Mr^2.

No idea how to start.
LVL 19
Who is Participating?

[Product update] Infrastructure Analysis Tool is now available with Business Accounts.Learn More

I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.



Treat the two questionbs separately.
Question 1
What is the angular momentum before the collision.
(The ball is a distance r below the pivot going a speed v)
That will be the angular momentum after the collision with the ball caught.

question 2

The energy (KE) of the ball is the total energy. That energy is converted to PE by the apparatus

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
BrianGEFF719Author Commented:
Thanks aburr, these quesions are acctually pretty easy you know where you need to end up :)

It's more than this solution.Get answers and train to solve all your tech problems - anytime, anywhere.Try it for free Edge Out The Competitionfor your dream job with proven skills and certifications.Get started today Stand Outas the employee with proven skills.Start learning today for free Move Your Career Forwardwith certification training in the latest technologies.Start your trial today
Math / Science

From novice to tech pro — start learning today.