How Does Collision Affect Angular Speed in Rotational Motion?

AI Thread Summary
In the discussion on how collision affects angular speed in rotational motion, a particle collides with a disk, causing it to rotate. The mass of the particle is 25 grams, moving at 12 m/s, while the disk has a mass of 500 grams and a radius of 11 cm. Participants confirm that moments of inertia can be added together, allowing for the calculation of the total moment of inertia by breaking the objects into parts. This approach is based on the integral form of moment of inertia, which involves summing the contributions from each segment. The discussion emphasizes the importance of understanding how to combine these moments to determine the angular speed post-collision.
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Homework Statement


In the figure, a small particle of mass m = 25 grams moving at speed of v0 = 12 m/s sticks to the edge of a disk of mass M = 500 grams and radius = 11 cm. The disk then rotates freely about its axis as a result of the collision. (The disk is on an axle.) Find the angular speed after the collision.
See Figure 1

The Attempt at a Solution


can I break up a moment of inertia and add its parts?
I = Idisk + Iparticle
 

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Yes, moments of inertia add. It is after all an integral of the form

\int r^2 \, dm

so you're free to break up an object into chunks, find the moment of inertia of each part and then sum them up altogether in the end.
 

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