A uniform disk of mass 19 kg and radius 0.6 m is free to rotated about an axis perpendicular to its center. A constant force of size 165 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 181 full rotations. What is the angular momentum of the disk after those rotations are complete, in kg m2/s? It could be useful to you to know that the rotational inertia of a uniform disk is 1/2 M R2. (Please answer to the fourth decimal place - i.e 14.3225)
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 uniform disk of mass 19 kg and radius 0.6 m is free to rotated about an axis perpendicular to its center. A constant force of size 165 N acts at the edge of the disk, in a direction tangent to that edge. The force acts until the disk has completed 181 full rotations. What is the
(Please answer to the fourth decimal place - i.e 14.3225)
Answer:
Let the mass of the disk be M, the radius of the disk be R, the magnitude of the force applied on the disk be F, the number of rotations performed by the disk be n, the initial angular velocity of the disk be ω0, and the angular velocity of the disk after 181 rotations be ω.
Assumption:
The disk was initially in the state of rest.
The torque τ of the applied force is given by the following equation.
Here, α is the angular acceleration, and I is the moment of inertia of the disk about the vertical axis through the center of the disk.
The angular velocity of the disk after 181 revolution is given by the following equation.
Here, Ө is the total angular displacement.
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