Inertia in the Brazil nut problem

Y Nahmad-Molinari1, G Canul-Chay, J C Ruiz-Suárez

  • 1Departamento de Física Aplicada, CINVESTAV-IPN, Unidad Mérida, AP 73 Cordemex, Mérida, Yucatán 97310, Mexico.

Related Concept Videos

Moments of Inertia: Problem Solving01:14

Moments of Inertia: Problem Solving

The second moment of an area, also known as the moment of inertia of an area, is a geometric property of a shape that reflects its resistance to change. The moment of inertia of an area can be calculated for both two-dimensional and three-dimensional shapes. The moment of inertia of an area is calculated by taking the sum of the product of the area and the square of its distance from a chosen axis of rotation. For two-dimensional shapes, the moment of inertia can be expressed as a single...
Product of Inertia for an Area01:13

Product of Inertia for an Area

Mechanical engineering involves making use of correct calculations to ensure that machines and structures are sturdy and long-lasting. One such calculation is the product of inertia for an area. It is a measure of how the mass of a structure is distributed around its centroid. It determines the structure's ability to resist rotational forces and affects the magnitude and direction of the stresses it experiences when subjected to external forces.
To calculate the product of inertia for any...
Mass Moment of Inertia: Problem Solving01:13

Mass Moment of Inertia: Problem Solving

Knowing how to determine the moment of inertia in a wheel's axle can be invaluable in engineering and automotive applications. It provides an understanding of how changes in geometry, mass, and radius can impact its performance.
The axle can be approximated to a solid cylinder with longitudinal and perpendicular axes. Initially, a thin disc is considered parallel to the circular face of the cylinder.
Principle of Angular Impulse and Momentum: Problem Solving01:19

Principle of Angular Impulse and Momentum: Problem Solving

Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, then the final velocity of the mass for time t can be determined using the principle of angular impulse and momentum.
Initially, a free-body diagram of the system is drawn to illustrate all the forces acting upon the system, providing a crucial understanding of the dynamics at play. Then, the principle of angular impulse and momentum is...
Moments and Product of Inertia01:23

Moments and Product of Inertia

The calculation of the moment of inertia for a differential element within a rigid body involves multiplying the element's mass by the square of the minimum distance from any one of the three-coordinate axes to the said element. This is a process that can be extended to cover the entire mass of the body by simply integrating the expression, thereby ascertaining the body's moment of inertia.
Inertia Tensor01:24

Inertia Tensor

The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...