A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M, radius R, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F. The coefficient of friction between the yoyo and the tabletop is μ. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. Determine an expression for the magntiude of the tourqe t excerted by the string about the contact point of the yo-yo with the table. Determine the magnitude of the linear accerlation of the center of the mass of the yo-yo the moment the strings became taught. Determine an expression for the moment of inertia of the yo-yo about the contact point with the table.
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 yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M, radius R, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F. The coefficient of friction between the yoyo and the tabletop is μ. The tension in the string is not sufficient to cause the yoyo to leave the tabletop.
Determine an expression for the magntiude of the tourqe t excerted by the string about the contact point of the yo-yo with the table.
Determine the magnitude of the linear accerlation of the center of the mass of the yo-yo the moment the strings became taught.
Determine an expression for the moment of inertia of the yo-yo about the contact point with the table.
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