A bullet of mass mB= 1.00·10‒2kg is moving with a speed of 100. m/s when it collides with...

Determine the angular velocity of the bullet-rod system after the collision. Also, determine the loss in kinetic energy in the collision.

SKETCH

The figure shows the rod pivots about an axis going through its center of mass, when the bullet collides with it.

RESEARCH:

Initial angular momentum of the system,

Moment of inertia of the rod,

As the bullet hits the rod at from the center, then the moment of inertia of rod when the bullet in the rod is

The final moment of inertial of the system

The translational kinetic energy of the bullet,

The rotational kinetic energy of the bullet and rod together,

SIMPLIFY:

(a) From the law of conservation of angular momentum, we have

(b) The loss in kinetic energy during the collision is given by

GIVEN DATA:

Mass of the bullet,

Mass of the rod,

Length of the rod,

Speed of the bullet,

CALCULATE:

(a) The angular velocity of the bullet-rod system after the collision can be calculated as

The moment of inertia of the system after collision can be calculated as

Then, the loss in kinetic energy during the collision can be calculated as

Here, the negative sign indicates that the loss in kinetic energy.