A thin rod of length L = 5 m and mass m has a linear density X(x) = Ax³ where x is the distance from the rod's left end. X(x) has units of kg/m and A = 6.38 with appropriate units that can't be displayed nicely due to Canvas limitations. Calculate the rod's moment of inertia I about an axis through x = 0 and perpendicular to the rod's length. (Hint: Evaluate the integral I = fr² dm where r = x is the distance from the axis to each element of mass dm = X(x) dx. Note: The rod's total mass mass m isn't needed but, if you would like to know it, you can find it by evaluating the integral m = f dm = f (x) dx.) I = kg m² .
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.
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