Rotational Energy, finding speed of rotation. Simple Problem.

And what is the angular momentum of this quantity in the center of mass frame of reference?In summary, the problem involves a pole sliding on a frictionless surface and colliding with a mass at one end, resulting in the two masses sticking together. The question asks for the angular velocity of the combined system after the collision. Since the collision is plastic, conservation of energy cannot be used. Instead, conservation of momentum is used, which is always conserved in collisions. Solving in the center of mass frame of reference may simplify the problem.
  • #1

Homework Statement

A pole P (300kg, length = 12m) is sliding on a frictionless surface at 8.28m/s. The pole's velocity is perpendicular to the poles length. A mass N (.5kg) collides with one end of the pole at 1043m/s and sticks.

How fast does the pole rotate after the collision?

Homework Equations

I'm assuming conservation of energy.

Kinetic energy: .5 x M x V2

Rotational Energy: .5 x I x w2

Where I = moment of inertia = 1/12M x L2 (radius was not given in the problem, I'm assuming the moment of inertia for a thin rod)

w = angular speed of rotation

The Attempt at a Solution

Pole's kinetic energy before impact:

.5 x 300kg x 8.28m/s2

Pole's kinetic + rotational energy after impact:

.5 x 300.5kg x v2 + .5 x 1/12*(300.5kg x (12m)2)w2

Due to the conservation of energy:

.5 x 300kg x 8.28m/s2 = .5 x 300.5kg x v2 + .5 x 1/12*(300.5kg x (12m)2)w2

I'm assuming the pole's center of mass is not significantly changed after the collision.

I also know that w(angular speed) = VCenter Mass/R

However, using this strategy, I result with two unknowns within my equation.

Any help with this is greatly appreciated.
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  • #2
This is a collision. Energy is sometimes conserved in a collision but not when the masses stick together. What quantity other than energy is conserved in a collision, even when the masses stick together?

Are you sure the initial speed of the mass is 1043 m/s? It sounds awfully large.
  • #3
As kuruman said, assuming conservation of energy is incorrect. In fact, in such collisions where the two bodies stick together, so-called 'plastic' collisions, mechanical energy is never conserved (You can prove this by considering a plastic collision between two masses, m1 and m2, in their center of mass system. The total momentum is 0 in this particular system, and yet you have kinetic energy prior to the collision, and none afterwards!)

As for this problem, my suggestion is for you to try and solve it from the system moving along with the pole if you don't succeed in solving from the laboratory system. Things may prove a bit more simple.
In fact, since the question only asks you for the angular velocity of the rod+mass after the collision, solving from the center of mass system is even preferable.

Like kuruman asked, what quantity is always conserved in collisions, even when they're plastic?
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