A rigid bearing assembly with a point mass m = 1.15 kg, suspended at the end of a thin rod of length l = 0.750 m, is forced to rotate uniformly with angular velocity ω = 3.80 rad/s about a vertical axis. See the figure below. The angle between the rotation axis and the rod is θ. Neglect the inertia of the bearing and of the rod connecting it to the mass. Neglect friction. Include the effects of the uniform force of gravity. What is the magnitude of the angular momentum of the system (due to the point mass) about the vertical axis of rotation of the bearing?
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 rigid bearing assembly with a point mass m = 1.15 kg, suspended at the end of a thin rod of length l = 0.750 m, is forced to rotate uniformly with
Step by step
Solved in 2 steps with 2 images
