Conserve angular momentum, then audit energy

A uniform rod of mass 3 kg and length 1 m is at rest about a fixed ideal end pivot. A 1/3 kg particle moving at 6 m/s strikes the free end perpendicular to the rod and sticks.

How much kinetic energy is lost during the collision?

Organize the givens & assumptions

Rod: 3 kg, 1 m
Particle: 1/3 kg, 6 m/s
Tangential hit at the free end

Short collision; all external angular impulses about the fixed pivot are negligible; no torque impulse from the ideal pivot; sticking is inelastic.

A $0\ \mathrm J$
B $1.5\ \mathrm J$
C $4.5\ \mathrm J$
D $6\ \mathrm J$

Try it on paper first. Free sample problems in every collection include the complete reasoning: find one in this collection →