Angular Velocity of Ballistic Cylinder After Bullet Impact

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SUMMARY

The discussion focuses on calculating the angular velocity of a solid cylinder after being impacted by a bullet. A 15.0 g bullet traveling at 456.1 m/s strikes a 21.1 kg cylinder with a radius of 0.31 m, positioned on a fixed vertical axis. The bullet adheres to the cylinder at a distance of 6.20 cm from the center. The relevant equations include angular momentum (L = r x p), moment of inertia (I = c*M*L^2), and the relationship between angular momentum and angular velocity (L = Iw). The user attempted to calculate L and I but encountered difficulties in deriving the angular velocity.

PREREQUISITES
  • Understanding of angular momentum and its calculation.
  • Familiarity with moment of inertia and its dependence on mass distribution.
  • Knowledge of the relationship between linear momentum and angular momentum.
  • Basic proficiency in physics equations related to rotational motion.
NEXT STEPS
  • Review the principles of angular momentum conservation in collisions.
  • Study the calculation of moment of inertia for various shapes, including cylinders.
  • Learn how to apply the right-hand rule for determining angular velocity direction.
  • Explore detailed examples of ballistic impacts and their effects on rotational motion.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of rotational motion following an impact event.

Ron Burgundy
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Homework Statement


A 15.0 g bullet is fired at 456.1 m/s into a solid cylinder of mass 21.1 kg and a radius 0.31 m. The cylinder is initially at rest and is mounted on fixed vertical axis that runs through it's center of mass.
The line of motion of the bullet is perpendicular to the axle and at a distance 6.20 cm from the center. Find the angular velocity of the system after the bullet strikes and adheres to the surface of the cylinder.


Homework Equations


L=r x p
I=c*M*L^2
L=Iw


The Attempt at a Solution


I tried to first find L by r*p*cos(theta). Then I calculated I, which I calculate to be 1.01. Then I divided L by I but it did not work. Help?
 
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