Physics of Motion

3 Key excerpts on "Physics of Motion"

• 

  eBook - ePub

  Reasoning About Luck

  • Vinay Ambegaokar(Author)
  • 2017(Publication Date)
  • Dover Publications

    (Publisher)

  6

  Forces, motion, and energy

  ... the whole burden of philosophy seems to consist in this – from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena ... Isaac Newton

  Probability enters theoretical physics in two important ways: in the theory of heat, which is a manifestation of the irregular motions of the microscopic constituents of matter; and, in quantum mechanics, where it plays the bizarre but, as far as we know, fundamental role already briefly mentioned in the discussion of radioactive decay.

  Before we can understand heat, we have to understand motion. What makes objects move, and how do they move? Isaac Newton, in the course of explaining the motion of planets and of things around us that we can see and feel with our unaided senses, answered these questions for such motions three centuries ago. The science he founded has come to be called classical or Newtonian mechanics, to distinguish it from quantum mechanics, the theory of motion in the atomic and sub-atomic world.

  Classical mechanics is summarized in Newton’s laws’ of motion. These will here be illustrated by an example involving the gravitational attraction, described by Newton’s ‘law’ of gravitation. In the brief description that follows, I shall attempt to show that these laws of nature: (i) unify apparently unrelated phenomena – like the motion of the moon and the fall of an apple; (ii) make simple but astonishing quantitative connections – between, for example, the rate of the moon’s revolution around the earth and the numerical value of the acceleration in an apple’s fall; and (iii), suggest new and useful concepts – here kinetic energy, potential energy, and, more generally, energy – which provide access to unexplored territory.

  To say that an object moves is to say that its position in space changes with time. This can only be given meaning by referring it to some fixed point. Imagine a straight line directed from such a fixed point to the place where our object is. This directed line is called the position ‘vector’ of the object. The word vector is used to indicate something that has a magnitude and a direction. We shall encounter other vector quantities soon. Two vectors are said to be equal when they have the same magnitude and

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Doing Physics with Scientific Notebook

  A Problem Solving Approach

  • Joseph Gallant(Author)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Chapter 5

  Newton’s Laws of Motion

  In the previous chapters on kinematics, we described motion in a quantitative sense. Once we know an object’s acceleration, we can describe its motion in terms of position, velocity, and time. Knowing how its motion changes lets us calculate how far, how fast, and how long the object moves.

  Now we move to a branch of physics known as dynamics. Dynamics is the study of the effects of forces on an object’s motion. Dynamics explains changes in motion by relating the cause of the changes (forces) to the effect (acceleration). Newton’s Second Law provides the rule relating the acceleration to the net force.

  There are three ingredients to Newton’s Second Law: the object’s acceleration, mass, and the net force acting on it. As we discussed in Chapter 2, the object’s acceleration is the rate of change in its velocity. Mass is a property of the object that determines how much change the net force produces. An object’s mass tells you how difficult it is to change its velocity and how much matter it has.

  A force is a push or a pull that can cause changes in motion. Forces are vectors, so they have magnitude and direction. This is consistent with your experience. When you exert a force on something, two things matter: how hard you push or pull and which way. Often objects have more than one force acting on them. The net force acting on an object is the vector sum of all the forces acting on it.

  Newton’s First Law

  Newton’s First Law tells us what happens when there is no net force acting on an object.

  Newton’s 1st Law: An object will remain in a state of rest or continue in motion at a constant velocity unless compelled to change by a non-zero net force.

  When there is no net force acting on the object, there is no change in the object’s velocity. If it is at rest, it remains at rest. If it is moving, it keeps moving at constant velocity. Since velocity is a vector, constant velocity means no change in both speed and direction. Motion at constant velocity is motion in a straight line at a constant speed.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Classical Mechanics

  A Computational Approach with Examples Using Mathematica and Python

  • Christopher W. Kulp, Vasilis Pagonis(Authors)
  • 2020(Publication Date)
  • CRC Press

    (Publisher)

  We also know from everyday experiences that there is a direct linear relationship between force and acceleration. For example, a 4 N net force will cause a 1 kg object to accelerate 4 m/s 2. Of course, the acceleration is caused by the vector sum of the forces. When you hold your cell phone, you are exerting a force upwards that matches the downward force of gravity, hence the two forces are equal in magnitude but opposite in direction, and therefore, their sum is zero. Hence, the cell phone does not accelerate. We have now laid out all of the tools needed to describe and explain an object’s motion. Next, we will discuss the core topic of classical mechanics, Newton’s Laws of Motion, which will explain the role of force and mass in determining the motion of an object. 1.3 Newton’s Laws of Motion Isaac Newton (1642–1727) developed both calculus and the foundations for classical mechanics. Newton’s book, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) was published in 1687 and is considered to be one of the most important works in the history of modern science. In the Principia, Newton stated his three laws of motion. Newton’s laws of motion are vital tools that allow us not only to explain why objects move the way that they do, but they also provide us with a means of predicting an object’s motion. In classical mechanics, the importance of Newton’s laws cannot be overstated; they are worth committing to memory. As you solve problems in this book, ask yourself how Newton’s laws are involved in the setup and solution to each problem

  Sign up to read

  Learn more about book