 # DYNAMICS The motion of a body is affected by other bodies present in the universe. This influence is called an interaction. vectors: force torque impulse.

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DYNAMICS The motion of a body is affected by other bodies present in the universe. This influence is called an interaction. vectors: force torque impulse scalars: work power heat There are a few ways to describe this interaction by mathematical models:

INERTIA Both the nature of the interaction and the characteristics of the object determine the effect of the interaction on the motion of the object. The “resistance” to change of motion is called inertia. Mass is a scalar quantity assigned to the inertial property of a body inertia

THE FIRST LAW OF MOTION If a particle does not interact with other bodies, it is possible to find a reference frame in which that particle has zero acceleration. (The 1729 translation by Andrew Motte from “Philosophiae Naturalis Principia Mathematica”: “Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.”) Sir Isaac Newton (1642 - 1727)

THE SECOND LAW OF MOTION In an inertial reference frame, the acceleration of a particle is proportional to the net force (the sum of all forces) exerted on the particle and inversely proportional to the mass of the particle. F 41 F net F 42 F 43 a 1 4 3 2 (“The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”) lunar lander

THE THIRD LAW OF MOTION If one body exerts a force on another body, the second body exerts an opposite force on the first one. (“To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”) F 21 F 12 1 2

FUNDAMENTAL FORCES On the microscopic scale there are only four kinds of interaction between particles: gravitational electromagnetic strong weak

GRAVITY A particle with mass m 1, separated from a particle with mass m 1 exerts an attractive force (vector) on the other particle F 21 1 2 r 12 (Objects with spherically distributed mass, also obey the above equations with r representing the distance between the centers of the objects. The force is exerted toward the center of the object exerting the force.) gravity

WEIGHT The product of the mass of an object and the free fall acceleration at the location of the object is called the weight of the object: W on earth g = 9.80 m/s 2 On a planet with radius R and mass M the weight of a body is approximately equal to the gravitational force exerted on the object by the planet.

NORMAL FORCE The normal force is the vector component of a force that a rigid surface exerts (due to deformation; strain) on an object with which it is in contact, namely, in the direction perpendicular to the surface. W N The normal force prevents objects from crossing the surface, therefore it is dependent on the other forces applied to the body. F net

STATIC FRICTION Static frictional force is a component of a force that a rigid surface exerts (due to strain) on the surface of an object with which it is in contact, namely, in the direction parallel to the surface. Within certain limits the static friction (interaction) prevents the object's surface from moving along the rigid surface. W N fsfs F

KINETIC FRICTION Kinetic frictional force is a component of a force that a rigid surface exerts (due to deformation) on the sliding surface of an object with which it is in contact, namely, in the direction parallel to the surface. W N fkfk F net F ext f f s = -F ext f s =  k N static kinetic friction

TENSION Tension force is an interaction that a surface exerts (due to deformation; strain) on an object with which it is in contact, namely, in the direction perpendicular to the surface. Tension force prevents the object from leaving the surface, therefore it is dependent on the other forces applied to the body. T spring

Nicolaus Copernicus 1473-1543 Galileo Gallilei 1564-1642 Johannes Kepler 1571-1630 Sir Isaac Newton 1642 - 1727 How to weigh the earth? Henry Cavendish 1731-1810

(where ) inertial “forces” O x y z  O’ x’ y’ z’ R r’ position: the rate of change of the (primed) frame base : Newton’s second law in a non-inertial reference frame: acceleration: velocity:

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