A 103 kg horizontal platform is a uniform disk of radius 1.55 m and can rotate about the vertical axis through its center. A 65.7 kg person stands on the platform at a distance of 1.05 m from the center , and a 28.1 kg dog sits on the platform near the person 1.31 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.
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 103 kg horizontal platform is a uniform disk of radius 1.55 m and can rotate about the vertical axis through its center. A 65.7 kg person stands on the platform at a distance of 1.05 m from the center , and a 28.1 kg dog sits on the platform near the person 1.31 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.
B) A uniform thin a rod of mass M=3.25 kg pivots about an axis through its center and perpendicular to its length. Two small bodies, each of mass m= 0.245 kg, are attached to the ends of the rod. What must the length L of the rod be so that the moment of the inertia of the three body system with respect to the described axis is I = 0.805 kg.m^2 ?
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