2. A yo-yo consists of two solid disks, each of mass M and radius 3R. The two disks are connected by a rod of radius R and negligible mass. Assume the yo-yo starts at rest. a. Use the view on the right to draw the extended free body diagram for the yo-yo. 3R b. What is the moment of inertia of the yo-yo about an axis through its symmetry axis? м м c. Write Newton's 2nd law for the yo-yo. Choose your coordinate system carefully. d. Write the rotational form of Newton's 2nd law for the yo-yo. Treat the center of mass as being at the axis of rotation. Choose the positive direction of the rotation so a is positive. e. The point where the yoyo is momentarily at rest is where the string contacts the rod of the yo-yo. Use this to obtain a relation between the acceleration of the center of mass and the angular acceleration. f. Determine the linear acceleration of the yo-yo.
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.
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