• A student on a piano stool rotates freely with an angular speed of2.95 rev>s. The student holds a 1.25-kg mass in each outstretchedarm, 0.759 m from the axis of rotation. The combined momentof inertia of the student and the stool, ignoring the two masses, is5.43 kg # m2, a value that remains constant. (a) As the student pullshis arms inward, his angular speed increases to 3.54 rev>s. How farare the masses from the axis of rotation at this time, consideringthe masses to be points? (b) Calculate the initial and final kineticenergies of the 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 student on a piano stool rotates freely with an angular speed of
2.95 rev>s. The student holds a 1.25-kg mass in each outstretched
arm, 0.759 m from the axis of rotation. The combined moment
of inertia of the student and the stool, ignoring the two masses, is
5.43 kg # m2
, a value that remains constant. (a) As the student pulls
his arms inward, his angular speed increases to 3.54 rev>s. How far
are the masses from the axis of rotation at this time, considering
the masses to be points? (b) Calculate the initial and final kinetic
energies of the system.
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