A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. Afriend spins the front wheel, of radius R, and observes that drops of water fly oiltangentially in an upward direction when the drops are at the same level as the centerof the wheel. She measures the height reached by drops moving vertically (Fig.P10.74). A drop that breaks loose from the tire on one turn rises a distance h1 abovethe tangent point. A drop that breaks loose on the next turn rises a distance h2 < h1above the tangent point. The height to which the drops rise decreases because theangular speed of the wheel decreases. From this information, determine themagnitude of the average angular acceleration of the wheel.
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 bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A
friend spins the front wheel, of radius R, and observes that drops of water fly oil
tangentially in an upward direction when the drops are at the same level as the center
of the wheel. She measures the height reached by drops moving vertically (Fig.
P10.74). A drop that breaks loose from the tire on one turn rises a distance h1 above
the tangent point. A drop that breaks loose on the next turn rises a distance h2 < h1
above the tangent point. The height to which the drops rise decreases because the
angular speed of the wheel decreases. From this information, determine the
magnitude of the average
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