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Collisions in rotation
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A bullet embedding in a rotating body conserves angular momentum.
A bullet hitting a rod or door conserves angular momentum about the pivot (not linear momentum, because the pivot exerts an impulse).
Bullet mv·d = Iω after embedding.
Energy is lost in the collision.
In more detail
In collisions involving rotating objects, both linear and angular momentum may be conserved, depending on the forces. Friction and impulsive forces at the contact point change angular momentum.
Real-world uses
- Analysing a ball hitting the ground and starting to roll.
- Billiard cue impacts that impart spin to the ball.
- When a bullet lodges in a spinning disc, the combined object spins more slowly, because the bullet adds mass far from the axis.
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Frequently asked questions
Are both momenta conserved?
Only if no external forces or torques act on the system.
What causes the ball to spin after a hit?
A friction force at the contact point produces a torque that adds spin.
Is angular momentum conserved in this collision?
Yes, if there is no external torque on the system. The bullet's angular momentum adds to the disc's and the total is preserved.
Related topics in Rotational Motion
Torque and angular momentum · Conservation of angular momentum · Spinning skater and diver · Precession of a gyroscope · Nutation · Rotation of the Earth