The picture shows a system composed of a swivel chair, a person on the chair and the bicycle wheel being held at armlength. The moment of inertia of the person and swivel chair is I0. The moment of inertia of the bicycle wheel around its center axis is I1. (a) The wheel is horizontal at a distance L from thechair axis. Give the total moment of inertia of the system around the swivel axis. (b) The wheel is rotated at w1, vector pointing up, and the chair is not rotating. Give the total angular momentum of the system. (c) The person flips the wheel upside down. Give the bicycle wheel’s new rotation speed and direction, and give the system’s rotation speed, w0 , and direction. Assume that the chair swivel has no friction and identify the components of the total torque that are always zero.
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.
The picture shows a system composed of a swivel chair, a person on the chair and the bicycle wheel being held at armlength. The moment of inertia of the person and swivel chair is I0. The moment of inertia of the bicycle wheel around its center axis is I1.
(a) The wheel is horizontal at a distance L from thechair axis. Give the total moment of inertia of the system around the swivel axis.
(b) The wheel is rotated at w1, vector pointing up, and the chair is not rotating. Give the total
(c) The person flips the wheel upside down. Give the bicycle wheel’s new rotation speed and direction, and give the system’s rotation speed, w0 , and direction. Assume that the chair swivel has no friction and identify the components of the total torque that are always zero.
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Can you explain how the parallel axial theorem applies to a? The wheel is spinning around its own axis within the system around the center axis.
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