A 100 kg uniform horizontal disk of radius 5.50 m tums without friction at 2.85 rev/s on a vertical axis through its center, as in the figure below. A feedback mechanis seses the angular speed of the disk, and a drive motor at A ensures that the angular speed remain constant while a 1.20 kg block on top of the dick sides outward in a radal slot The 120 kg block starts at the center of the disk at time t 0 and moves outward with constant speed 1.25 cm/s relative to the disk until it reaches the edge at t 520 s. The sliding block experiences no friction. Its motion is constrained to have constant radial speed by a brake at 8, producing tension in a light string tied to the block. (a) Find the torque as a function of time that the drive motor must provide while the block is sliding. rN-m (b) Find the value of this torque at t 520 s, just before the sliding block finishes its motion. N-m (c) Find the power which the drive motor must deliver as a function of time. eW/s
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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