Projectile against a rod: three cases compared

This is perhaps the most instructive of all rotational-mechanics problems: the same physical setup — a projectile striking a rod — gives rise to three completely different problems depending on two choices: is the rod pivoted or free? is the collision inelastic or elastic? Depending on the answers, which quantities are conserved changes, and hence how many equations we have and which unknowns we can determine. This section compares the three cases on the same setup, then draws the general rules for when to use $L = I\omega$ and $E_\text{cin} = \tfrac{1}{2}I\omega^2$.

• The common setup
• Case 1: inelastic collision with pivoted rod
• Case 2: elastic collision with pivoted rod
• Case 3: elastic collision with rod free on a rail
• Summary of the conservation laws
• When to use L = Iω and Ecin = ½Iω²
• Disc with an unwinding string
• The skater who pulls in her arms

Try it — interactive simulation