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

[hidemi]

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.

 

[haruspex]

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.

 

[hidemi]

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.

 

[haruspex]

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.

 

[hidemi]

If it is a perfectly elastic bounce, yes.

Thank you so much.