A bicycle wheel is essentially a hoop with a bunch of sticks (spokes) connecting the hoop to the center axel. Let's say the radius of the hoop is R and the mass of the hoop is 10M. Each spokes has a mass of M/6 and there are 18 spokes. a) What is the moment of inertia about the center of mass? b) A massless ropes of length 5R is now tied about the edge of the wheel and the system is allowed to swing(like a pendulum) about the end of the rope. What is the moment of inertia of this system about where the rope is held?
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 essentially a hoop with a bunch of sticks (spokes) connecting the hoop to the center axel. Let's say the radius of the hoop is R and the mass of the hoop is 10M. Each spokes has a mass of M/6 and there are 18 spokes. a) What is the moment of inertia about the center of mass? b) A massless ropes of length 5R is now tied about the edge of the wheel and the system is allowed to swing(like a pendulum) about the end of the rope. What is the moment of inertia of this system about where the rope is held?
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