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66 PHYSICS directed upwards (not shown in the gravity on the mass in (a) or (b) and the normal figure). force on the mass by the floor are not action- (ii) the force on the floor by the system reaction pairs. These forces happen to be equal (action); the force on the system by the and opposite for (a) since the mass is at rest. floor (reaction). In addition, for (b), the They are not so for case (b), as seen already. force on the block by the cylinder and The weight of the system is 270 N, while the the force on the cylinder by the block normal force R′ is 267.3 N. ⊳ also constitute an action-reaction pair. The practice of drawing free-body diagrams is The important thing to remember is that an of great help in solving problems in mechanics. action-reaction pair consists of mutual forces It allows you to clearly define your system and which are always equal and opposite between consider all forces on the system due to objects two bodies. Two forces on the same body which that are not part of the system itself. A number happen to be equal and opposite can never of exercises in this and subsequent chapters will constitute an action-reaction pair. The force of help you cultivate this practice. SUMMARY 1. Aristotle’s view that a force is necessary to keep a body in uniform motion is wrong. A force is necessary in practice to counter the opposing force of friction. 2. Galileo extrapolated simple observations on motion of bodies on inclined planes, and arrived at the law of inertia. Newton’s first law of motion is the same law rephrased thus: “Everybody 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”. In simple terms, the First Law is “If external force on a body is zero, its acceleration is zero”. 3. Momentum (p) of a body is the product of its mass (m) and velocity (v) : p = m v 4. Newton’s second law of motion : The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.s F = k dp = k m a dt where F is the net external force on the body and a its acceleration. We set the constant of proportionality k = 1 in SI units. Then dp F = = ma dt The SI unit of force is newton : 1 N = 1 kg m s . (a) The second law is consistent with the First Law (F = 0 implies a = 0) (b) It is a vector equation (c) It is applicable to a particle, and also to a body or a system of particles, provided F is the total external force on the system and a is the acceleration of the system as a whole. (d) F at a point at a certain instant determines a at the same point at that instant. That is the Second Law is a local law; a at an instant does not depend on the history of motion. 4. Impulse is the product of force and time which equals change in momentum. The notion of impulse is useful when a large force acts for a short time to produce a measurable change in momentum. Since the time of action of the force is very short, one can assume that there is no appreciable change in the position of the body during the action of the impulsive force. 6. Newton’s third law of motion: To every action, there is always an equal and opposite reaction Reprint 2026-27