A 0.0110 kg bullet is fired at v0=554 m/s into a solid cylinder of mass 17.1 kg and radius 0.290 m (moment of inertia: I=1/2mR2). The cylinder is initially at rest and is mounted on the fixed vertical axis that runs through its center of mass. The line of motion of the bullet is perpendicular to the axle and at a distance d=5.80 cm from the axis. Find the angular velocity of the system (in rad/sec) after the bullet strikes and adheres to the surface of the cylinder. (Hint: calculate the initial angular momentum of the bullet [around the axis] before it hits the cylinder; you should find that it depends only on v0 and d, but not on the cylinder's radius.)
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
Bullet fired into wheel
A 0.0110 kg bullet is fired at v0=554 m/s into a solid cylinder of mass 17.1 kg and radius 0.290 m (moment of inertia: I=1/2mR2). The cylinder is initially at rest and is mounted on the fixed vertical axis that runs through its center of mass. The line of motion of the bullet is perpendicular to the axle and at a distance d=5.80 cm from the axis. Find the
(Hint: calculate the initial
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