A window cleaner is pulling himself up to a pulley that consists of two disks welded together as shown. The person is currently pulling straight down on the rope in his hands with a force of magnitude 597.5 N. The other rope is also vertical and is attached to the person's center of mass. The person's mass is 88.3 kg, the pulley's total moment of inertia is 4.58 kg⋅m2, the radius of the small disk is 0.36 m, and the radius of the big disk is 0.71 m. What is the magnitude of the acceleration of the person's center of mass?
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 window cleaner is pulling himself up to a pulley that consists of two disks welded together as shown. The person is currently pulling straight down on the rope in his hands with a force of magnitude 597.5 N. The other rope is also vertical and is attached to the person's center of mass. The person's mass is 88.3 kg, the pulley's total moment of inertia is 4.58 kg⋅m2, the radius of the small disk is 0.36 m, and the radius of the big disk is 0.71 m.
What is the magnitude of the acceleration of the person's center of mass?
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