ANL - Introduction to Application of Newton's Laws

Application of Newton's Laws

Introduction

This unit will apply the lesson of motion and force to objects that travel in uniform circular pathways. Centripetal force will be introduced and defined as will centripetal acceleration. Newton's Law of Universal Gravitation is discussed in this unit because it is the force that causes the centripetal acceleration of an object orbiting the earth. We will learn the relationship between the masses of two objects, their distance apart, and the force that attracts the two objects. Kepler's Laws will be discussed and applied to objects that are orbiting around other masses.

Essential Questions

  1. What is the relationship between the radius of a circle and the speed of a particle to the magnitude of the centripetal acceleration?
  2. What is the direction of a particle's velocity and acceleration at any instant that is going through uniform circular motion?
  3. What are the components of the velocity and acceleration vectors of an object undergoing uniform circular motion?
  4. What are the forces acting on an object undergoing uniform horizontal or vertical circular motion?
  5. What is the the force that one spherically symmetrical mass exerts on another?
  6. What is the the strength of the gravitational field at a point outside a spherically symmetrical mass?
  7. What is the gravitational force inside and outside a uniform sphere and how does the field at the surface depend on the radius and density of the sphere?
  8. For an object in a circular orbit, how does the velocity, period of revolution, and acceleration depend on the radius?
  9. What is the relationship between kinetic, potential, and total energy for an object in a circular orbit?
  10. What are Kepler's three laws and how can they be used to describe the motion of an object in an elliptical orbit?
  11. How can the conservation of angular momentum be applied to determine the velocity and radial distance at any point in an orbit?
  12. How can the conservation of angular momentum and conservation of energy be used to relate the speeds of an object at the two extremes of an elliptical orbit?
  13. How can energy conservation be used to analyze the motion of an object moving straight away from or straight toward a planet?

Key Terms

  1. Centripetal Acceleration - The acceleration directed toward the center of a circular pathway.
  2. Centripetal Force - The net force directed toward the center of a circular pathway that causes an object to travel on that pathway.
  3. Universal Gravitational Constant -  6.67 x 10-11 LaTeX: \frac{Nm^2}{kg^2}Nm2kg2
  4. Aphelion - The point when a planet is farthest from the Sun in its orbit.
  5. Perihelion - The point when a planet is closest to the Sun in its orbit.

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