A bicycle wheel is mounted on a fixed, frictionless axle. A massless string is wound around the wheel's rim, and a constant horizontal force F of magnitude F starts pulling the string from the top of the wheel starting at time t=0 when the wheel is not rotating. Suppose that at some later time t the string has been pulled through a distance d. The wheel has moment of inertia I=kmr2, where k is a dimensionless number less than 1, m is the wheel's mass, and r is its radius. Assume that the string does not slip on the wheel. The force F pulling the string is constant; therefore the magnitude of the angular acceleration α of the wheel is constant for this configuration. Find the magnitude of the angular velocity ω of the wheel when the string has been pulled a distance d. Express the angular velocity ω of the wheel in terms of the displacement d, the magnitude F of the applied force, and the moment of inertia of the wheel Iw, if you've found such a solution. Otherwise, following the hints for this part should lead you to express the angular velocity ω of the wheel in terms of the displacement d, the wheel's radius r, and α.
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 wheel is mounted on a fixed, frictionless axle. A massless string is wound around the wheel's rim, and a constant horizontal force F of magnitude F starts pulling the string from the top of the wheel starting at time t=0 when the wheel is not rotating. Suppose that at some later time t the string has been pulled through a distance d. The wheel has moment of inertia I=kmr2, where k is a dimensionless number less than 1, m is the wheel's mass, and r is its radius. Assume that the string does not slip on the wheel.
The force F pulling the string is constant; therefore the magnitude of the
Find the magnitude of the
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