A cylinder with rotational inertia /₁ = 2.0 kgm² rotates clockwise about a vertical axis through its center with angular speed w₁ = 4.0 rad/s. A second cylinder with rotational inertia /2 = 1.0 kgm² rotates counter-clockwise about the same axis with angular speed w₂ = 8.0 rad/s. a) Assuming no external torques act on the system of cylinders, if the cylinders couple so they have the same rotational axis, what is the angular speed of the combination? Hint: Pick a direction for the angular momentum. Let counter-clockwise rotation correspond to a positive L and a clockwise rotation correspond to a negative L. Enter to 2 significant figures rad/s b) What percentage of the kinetic energy is lost during the coupling? Enter to 2 significant figures @=
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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