Law

• In the preceding Chapter, our concern was to describe the motion of a particle in space quantitatively. We saw that uniform motion needs the concept of velocity alone whereas non-uniform motion requires the concept of acceleration in addition.
• So far, we have not asked the question as to what governs the motion of bodies. In this chapter, we turn to this basic question.
• Force


  External agency needed to provide force to move a body from rest or retard/stop motion
• An external force is needed to put a stationary body in motion or stop a moving body, and some external agency is needed to provide this force. The external agency may or may not be in contact with the body.
• The question posed above appears to be simple. However, it took ages to answer it. Indeed, the correct answer to this question given by Galileo in the seventeenth century was the foundation of Newtonian mechanics, which signalled the birth of modern science.
• Aristotle's view


  An external force is required to keep a body in motion
• Aristotelian law of motion is flawed, as we shall see. However, it is a natural view that anyone would hold from common experience.
• The flaw in Aristotle's argument is that a moving toy car comes to rest because the external force of friction on the car by the floor opposes its motion. To counter this force, the child has to apply an external force on the car in the direction of motion.
• When the car is in uniform motion, there is no net external force acting on it: the force by the child cancels the force (friction) by the floor. The corollary is: if there were no friction, the child would not be required to apply any force to keep the toy car in uniform motion.
• Inertia


  Resistance to change. A body does not change its state of rest or uniform motion, unless an external force compels it to change that state.
• Newton's first law of motion

  Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.
• If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero only if there is a net external force on the body.
• For terrestrial phenomena, in particular, every object experiences gravitational force due to the earth. Also objects in motion generally experience friction, viscous drag, etc. If then, on earth, an object is at rest or in uniform linear motion, it is not because there are no forces acting on it, but because the various external forces cancel out i.e. add up to zero net external force.
• When the car is stationary, there is no net force acting on it. During pick-up, it accelerates. This must happen due to a net external force. Note, it has to be an external force. The acceleration of the car cannot be accounted for by any internal force.
• When the car moves with constant velocity, there is no net external force. The property of inertia contained in the First law is that a body continues in its state of rest or uniform motion unless acted upon by an external force.
• The net force acting on the astronaut, once he is out of the spaceship, is zero
• By the first law of motion the acceleration of the astronaut is zero
• Momentum


  The product of mass m and velocity v, denoted as p = mv
• For a given mass, the greater the speed, the greater is the opposing force needed to stop the body in a certain time
• The greater the change in the momentum in a given time, the greater is the force that needs to be applied
• The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts
• Second law of motion

  F = d(mv)/dt = ma
• In SI unit, force is one that causes an acceleration of 1 m/s^2 to a mass of 1 kg. This unit is known as newton: 1 N = 1 kg m/s^2
• The second law of motion is a vector law, equivalent to three equations, one for each component of the vectors
• The second law of motion applies to a single point particle, a rigid body, or a system of particles. The force F refers to the total external force on the system and a refers to the acceleration of the system as a whole
• The second law of motion is a local relation, meaning that force F at a point in space at a certain instant of time is related to acceleration a at that point at that instant
• Impulse


  The product of force and time duration, equal to the change in momentum
• Impulsive force is a large force acting for a short time to produce a finite change in momentum
• Impulse


  The product of force and time, which is the change in momentum of the body
• A large force acting for a short time to produce a finite change in momentum is called an impulsive force
• Impulse imparted to the ball = 3.6 N·s, in the direction from the batsman to the bowler
• Newton's Third Law of Motion

  Forces always occur in pairs. Force on a body A by B is equal and opposite to the force on the body B by A
• Action and reaction forces act on different bodies, not on the same body
• Internal forces in a body or a system of particles cancel away in pairs
• Conservation of Momentum


  The total momentum of an isolated system of interacting particles is conserved
• In an isolated system, mutual forces between pairs of particles can cause momentum change in individual particles, but the total momentum remains unchanged
• Equilibrium of a particle

  The net external force on the particle is zero
• Equilibrium under three concurrent forces requires that the vector sum of the three forces is zero
• Gravitational force


  Every object on the earth experiences the force of gravity due to the earth
• Contact forces


  Forces that arise due to contact between objects, including normal reaction and friction