How Does Collision Affect Angular Speed in Rotational Motion?

In summary, a small particle of mass 25 grams collides with a disk of mass 500 grams and radius 11 cm, causing the disk to rotate freely about its axis. The angular speed after the collision can be found by adding the moments of inertia of each part.
  • #1
uchicago2012
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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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  • #2
Yes, moments of inertia add. It is after all an integral of the form

[tex] \int r^2 \, dm [/tex]

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.
 

FAQ: How Does Collision Affect Angular Speed in Rotational Motion?

What is angular momentum conservation?

Angular momentum conservation is a fundamental principle in physics that states that the total angular momentum of a closed system remains constant over time. This means that the angular momentum of a system before and after an interaction or event remains the same.

How is angular momentum conserved?

Angular momentum is conserved through the law of conservation of momentum, which states that the total momentum of a closed system remains constant. This means that any changes in one object's momentum must be offset by changes in the momentum of another object in the system, resulting in a constant total momentum.

What is the relationship between angular momentum and rotational motion?

Angular momentum is a measure of an object's rotational motion. It is defined as the product of an object's moment of inertia and its angular velocity. This means that the faster an object rotates or the greater its mass is distributed from its axis of rotation, the greater its angular momentum will be.

Are there any real-life examples of angular momentum conservation?

Yes, there are many real-life examples of angular momentum conservation. One common example is the spinning of a figure skater. As the skater pulls their arms in towards their body, their moment of inertia decreases, causing their angular velocity to increase and thus conserving their angular momentum.

Can angular momentum be lost or gained?

No, angular momentum cannot be gained or lost in a closed system. This is due to the law of conservation of momentum, which states that the total momentum of a closed system remains constant. However, in an open system where external forces can act upon the system, angular momentum can be transferred in or out of the system.

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