A thin rod of length b is perpendicular to a wire passing through the z-axis and rotates around this wire with an angular velocity w, as shown in the figure. The wire pierces the rod at a distance b/3 from its end and at the point a(in the z direction, "k^" ) of the coordinate system used. The mass of the bar is m, its density is uniformly distributed over its length. There is no gravity in this problem. Give your answers in terms of (w, m, a, b, î, j, k) using the coordinate system in the figure (some of these may not be included in the answer) Find the components of the angular momentum L of the rod with respect to the origin (0) of the coordinate system?
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.
A thin rod of length b is perpendicular to a wire passing through the z-axis and rotates around this wire with an
Give your answers in terms of (w, m, a, b, î, j, k) using the coordinate system in the figure (some of these may not be included in the answer)
Find the components of the
Hint is given in the 2. figure
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