Re: angular momentum and inelastic collision

From: Timo Nieminen (timo_at_physics.uq.edu.au)
Date: 11/23/04 

Date: Tue, 23 Nov 2004 15:58:34 +1000

On Tue, 22 Nov 2004, quick wrote:

> 1) A merry-go-round is a common piece of playground equipment. A
> 3.0-m-diameter merry-go-round with a mass of 250 kg is spinning at 20
> rpm. John runs tangent to the merry-go-round at 5.0 m/s, in the same
> direction that it is turning, and jumps onto the outer edge. John's
> mass is 30 kg. What is the merry-go-round's angular velocity, in rpm,
> after John jumps on?
>
> i know how to solve it i could find the moment of inertia for john but
> i don't think that is easy to do.

Assume John is a point mass.

> 2) A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door
> at the edge opposite the hinge. The bullet embeds itself in the door,
> causing the door to swing open. What is the angular velocity of the
> door just after impact?
>
> i know this is an inelastic collision and i could find the velocity of
> the door after the impact but am not sure how to find the angular
> velocity since it is connected to the door.

Do it the same way as 1). Initial angular momentum of the door is zero.
Take all angular momenta about an axis through the hinges. If you can look
up the moment of inertia of a thin rectangular *** about an edge, it's
easy enough to calculate by integrating across the width.

Note that you can't treat it as a normal inelastic collision (ie find the
velocity of the door via conservation of momentum) since there is an
unknown force exterted on the door by the hinges. Since the moment of this
force is zero, there's no problem with using conservation of angular
momentum. 

-- 
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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