What is the final angular velocity of the system after the collision?

AI Thread Summary
The discussion centers on the application of conservation of energy in a collision scenario where two bodies stick together. It emphasizes that mechanical energy cannot be assumed to be conserved in inelastic collisions, as energy is absorbed during the coalescence. A hypothetical situation is presented where a ball bounces off a surface, illustrating that energy conservation applies only in perfectly elastic collisions. The participants agree that if the collision were elastic, conservation of energy could be used. Understanding the nature of the collision is crucial for determining the final angular velocity of the system.
hidemi
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Homework Statement
A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision?
(A) 8.1
(B) 2.0
(C) 6.1
(D) 4.2
(E) 10
Relevant Equations
Li = Lf = Iω
I calculated as attached and got it right. However, I just wonder why we can't use conservation of energy as the question has already specified 'frictionless', meaning no energy loss and energy distributed to the rotation only.
 

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hidemi said:
why we can't use conservation of energy
You should never assume conservation of mechanical energy without good cause.
The scenario in this question is a coalescence: the two bodies stick together after colliding. Imagine what would happen if they did not do so, e.g. if it were a rubber ball hitting a protrusion from a concrete drum. Clearly the ball would bounce off. The glue that holds them together in the actual question has therefore absorbed the energy that would have been associated with that rebound.
 
haruspex said:
You should never assume conservation of mechanical energy without good cause.
The scenario in this question is a coalescence: the two bodies stick together after colliding. Imagine what would happen if they did not do so, e.g. if it were a rubber ball hitting a protrusion from a concrete drum. Clearly the ball would bounce off. The glue that holds them together in the actual question has therefore absorbed the energy that would have been associated with that rebound.
Oh I see.
If the question rephrases a bit, the ball hits the cylinder and bounces off as well as the frictionless remains, then the conservation of energy can be established. Let me know if I'm right.
 
hidemi said:
If the question rephrases a bit, the ball hits the cylinder and bounces off as well as the frictionless remains, then the conservation of energy can be established.
If it is a perfectly elastic bounce, yes.
 
haruspex said:
If it is a perfectly elastic bounce, yes.
Thank you so much.
 
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