Key Concepts in Mechanics: Momentum, Collisions, and Circular Motion

Posted on Jan 28, 2025 in Physics

Key Concepts in Mechanics

Momentum and Collisions

Coefficient of Restitution: The negative ratio of the relative velocity after impact to the relative velocity before collision.

Completely Elastic Collision: A collision where kinetic energy remains constant.

Completely Inelastic Collision: A collision where the colliding bodies stick together and move off as a unit afterward.

Conservation of Momentum: The total momentum of colliding bodies before impact is equal to their total momentum after impact.

Elasticity: The vigor with which a body returns to its original shape after deformation is a measure of elasticity.

Impulse: A vector quantity equal in magnitude to the product of the force and the time in which it acts.

Momentum: A vector quantity equal in magnitude to the product of its mass (m) and its velocity (v).

Circular Motion

Centripetal: Means that the acceleration is always directed toward the center.

Centripetal Acceleration: Given by ac=v2/r, where v is the linear speed of a particle moving in a circular path of radius r.

Centripetal Force: The inward force necessary to maintain uniform circular motion.

Conical Pendulum: Consists of a mass (m) revolving in a horizontal circle with constant speed (v) at the end of a cord of length (L).

Critical Velocity: vc occurs when the tension in the rope reduces to zero (T1=0), and the entire centripetal force is provided by the weight (mg).

Frequency: The number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

Geosynchronous: Being or having an orbit around the Earth with a period equal to one sidereal day.

Gravitation

  • Gravitation:
    • a. The natural phenomenon of attraction between physical objects with mass; the weakest of the four fundamental forces of nature. Also called gravity.
    • b. The act or process of moving under the influence of this attraction.
  • Gravitational Field: The attractive effect, considered as extending throughout space, of matter on other matter.

Kepler’s Three Laws of Planetary Motion:

  • The path of the planets about the Sun is elliptical, with the center of the Sun being located at one focus. (The Law of Ellipses)
  • An imaginary line drawn from the center of the Sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)
  • The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the Sun. (The Law of Harmonies)

Linear Motion is Uniform Motion: It is the motion of the body in one dimension, and the moving body is considered as a particle.

Period: The time needed for one complete cycle of vibration to pass a given point.

Uniform Circular Motion: The motion of an object in a circle at a constant speed. As an object moves in a circle, it constantly changes its direction.

Newton’s Law of Universal Gravitation: States that a particle attracts every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Weight: Defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, w = mg.