Physics I: Chapter 5

Reference: Beginning Physics I




Resultant Force and Acceleration, Newton’s Second Law, Mass, Inertia, Weight, Centripetal Force, Banking Equation, Newton’s Law of Gravitation



For details on the following concepts, please consult CHAPTER 5.

The unbalanced force on an object causes its acceleration until it comes into balance. The acceleration continues with velocity increasing if the force is non-zero. When the unbalanced force vanishes, so does the acceleration, but the higher velocity continues at a constant rate unless some other resistance or counter force comes into play.

When a nonzero resultant force F acts on a given object, the consequent acceleration a always points in the direction of F. Also, for a given magnitude of F, the magnitude of a is the same no matter what the direction of the force. On the other hand, if the magnitude of F doubles, the magnitude of a doubles; if the magnitude of F triples, the magnitude of a triples; etc. Thus, the magnitude of a is proportional to the magnitude of F. The proportionality constant is called the mass m of the object. This is expressed as the equation,

F = ma.

This equation is the mathematical statement of Newton’s second law.

The mass controls the response of the object to a given magnitude force. A small mass means a large acceleration, a large means a small acceleration. In a sense, the mass is a measure of the resistance of an object to having its velocity changed. This resistance is referred to as the inertia of the object. The relative magnitude of different masses can easily be established by applying the same magnitude force to different objects and measuring their accelerations. Then

The mass is an indestructible and unchanging property of any object that stays with the object even when it is combined into larger units. In the same way, when an object is broken into smaller parts, the sum of masses of the parts equals the original mass.

Units of mass: Kilogram; 1 lbm = 0.45359 kg; 1 slug = 32.2 lbm = 14.7 kg

Inertia is the resistance of an object to having its velocity changed. The inertia is exhibited while the velocity is changing. It vanishes when the velocity settles back to a higher constant value. At higher velocity, the mass of the object reduces (per the theory of relativity) by the amount of inertia overcome by the force. But this reduction in mass is infinitesimal and ignored in mathematical calculations at the level of matter. The mass reduces to almost zero when the speed of light is reached.

The pull of gravity on an object is commonly called its weight. Weight and mass are proportional at a given point on earth’s surface.

When an object moves in uniform circular motion, it happens because it is continually being drawn toward the center of that path. The force drawing the object toward the center is called the centripetal force.

F = mv2/r

The banking equation gives the general relation among  (the banking angle), v (the velocity) and r (the radius of the curved path) that must hold in order to go around the curve, without the need for any frictional force. Note that the mass of vehicle does not enter the equation:


Newton’s Law of universal gravitation states that every particle of matter in the universe attracts every other particle of matter in the universe with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If we assume the proportional constant is G, the magnitude of this force is then


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