One end of a massless rigid rod of length ℓ is attached to a wooden block of mass M resting on a frictionless, horizontal tabletop, and the other end is attached to the table through a pivot (see figure below). A bullet of mass m traveling with a speed v in a direction perpendicular to the rod and parallel to the table impacts the block and embeds itself inside. (a) What is the angular momentum of this system around a vertical axis through the pivot after the collision? (Use any variable or symbol stated above as necessary. Enter your answer as an expression for magnitude.) L =
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.
One end of a massless rigid rod of length ℓ is attached to a wooden block of mass M resting on a frictionless, horizontal tabletop, and the other end is attached to the table through a pivot (see figure below). A bullet of mass m traveling with a speed v in a direction perpendicular to the rod and parallel to the table impacts the block and embeds itself inside.
L =
(b) What is the fraction of the bullet's initial kinetic energy that is lost to internal energy during the collision? (Use any variable or symbol stated above as necessary. Enter your answer as an expression for magnitude.)
| ΔK |
| Ki |
Given that:
The mass of the wooden block is .
The velocity is .
The mass of the bullet is .
It is required to find the angular momentum of this system around a vertical axis through the pivot after the collision and the fraction of kinetic energy that is lost.
Step by step
Solved in 4 steps
