1a. Several objects have the same mass and radius and are placed at the top of a hill of height ℎ. If all the objects are released from the same height ℎ at the same time, rank the order in which the objects reach the bottom of the hill, from first to last. The moment of inertia of each of the objects are listed below. If any of the objects tie, indicate that in your ranking. Object 1: Hoop Object 2: Solid Sphere Object 3: Disk Object 4: Hollow Object 5: Solid Cylinder Ihoop = MR2 Isolid sphere = (2/5)MR2 Idisk = (1/2)MR2 Ihollow = (2/3)MR2 Isolid cylinder = (1/2)MR2
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.
1a. Several objects have the same mass and radius and are placed at the top of a hill of height ℎ. If all the objects are released from the same height ℎ at the same time, rank the order in which the objects reach the bottom of the hill, from first to last. The moment of inertia of each of the objects are listed below. If any of the objects tie, indicate that in your ranking.
|
Object 1: Hoop |
Object 2: Solid Sphere |
Object 3: Disk |
Object 4: Hollow |
Object 5: Solid Cylinder |
|
Ihoop = MR2 |
Isolid sphere = (2/5)MR2 |
Idisk = (1/2)MR2 |
Ihollow = (2/3)MR2 |
Isolid cylinder = (1/2)MR2 |
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