A boy sits on a rotating seat while holding a pair of objects as shown in the figure below. The seat can rotate about a vertical axis with negligible friction. The moment of inertia of the boy, objects, and seat is 2.250 kg · m2 . The boy rotates with arms outstretched, making one complete turn every 1.260 s, arms outstretched. (a) Calculate the initial angular speed of the system. (b) As he rotates, the boy pulls the objects inward so that the new moment of inertia of the system (boy, objects, and seat) becomes 1.800 kg · m2 . Calculate the new angular speed of the system. (c) Calculate the work done by the boy on the system while pulling in the objects. (Ignore energy lost through dissipation in his muscles.
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 boy sits on a rotating seat while holding a pair of objects as shown in the figure below. The
seat can rotate about a vertical axis with negligible friction. The moment of inertia of the boy,
objects, and seat is 2.250 kg · m2
. The boy rotates with arms outstretched, making one
complete turn every 1.260 s, arms outstretched.
(a) Calculate the initial angular speed of the system.
(b) As he rotates, the boy pulls the objects inward so that the new moment of inertia of the
system (boy, objects, and seat) becomes 1.800 kg · m2
. Calculate the new angular speed of
the system.
(c) Calculate the work done by the boy on the system while pulling in the objects. (Ignore
energy lost through dissipation in his muscles.
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