Physics 1D03 - Lecture 61 Classroom Change Our class will be in Hamilton Hall 302 from now on !

Physics 1D03 - Lecture 62 Vector Review Scalars and Vectors Vector Components and Arithmetic

Physics 1D03 - Lecture 63 Physical quantities are classified as scalars, vectors, etc. Scalar : described by a real number with units examples: mass, charge, energy... Vector : described by a scalar (its magnitude) and a direction in space examples: displacement, velocity, force... Vectors have direction, and obey different rules of arithmetic.

Physics 1D03 - Lecture 64 Notation Scalars : ordinary or italic font (m, q, t...) Vectors : - Boldface font (v, a, F...) - arrow notation - underline (v, a, F...) Pay attention to notation : “constant v” and “constant v” mean different things!

Physics 1D03 - Lecture 65 Coordinate Systems In 2-D : describe a location in a plane by polar coordinates : distance r and angle  by Cartesian coordinates : distances x, y, parallel to axes with: x=rcosθ y=rsinθ These are the x and y components of r x y  r ( x, y ) 0 x y

Physics 1D03 - Lecture 66 Addition: AxAx AyAy ByBy BxBx ByBy BxBx AyAy AxAx CxCx CyCy If A + B = C, then: Three scalar equations from one vector equation! Tail to Head

Physics 1D03 - Lecture 67 Newton’s Laws of Motion Newton’s Laws Forces Mass and Weight

Physics 1D03 - Lecture 68 Newton’s First Law (Law of Inertia ) An isolated object, free from external forces, will continue moving at constant velocity, or remain at rest. Earlier, Aristotle said objects were “naturally” at rest, and needed a continuing push to keep moving. Galileo realized that motion at constant velocity is “natural”, and only changes in velocity require external causes. Objects in equilibrium (no net external force) also move at constant velocity.

Physics 1D03 - Lecture 69 Forces A force is a push or pull that tends to cause motion (more exactly, changes in motion) From the Second Law, force should have units of Force is a vector. In Newton’s dynamics, all influences on a particle from its surroundings are expressed as forces exerted on that particle.

Physics 1D03 - Lecture 610 Newton’s Second Law F net (or F total ) is the vector sum of all forces acting on the particle of mass m: The acceleration a is parallel to the total force, and proportional to it. The proportionality constant is the particle’s mass. Newton defines mass as a measure of an object’s inertia.

Physics 1D03 - Lecture 611 Contact Forces : direct contact is required examples - normal forces, friction, air resistance, buoyancy,... Non-Contact Forces : gravity, electromagnetic, weak and strong forces The gravitational force is also called weight and is measured in Newtons. Weight is proportional to mass : F w = mg, where g is the gravitational field (and is also the acceleration of an object in free fall).

Physics 1D03 - Lecture 612 Weight and Mass Weight is a force; it can be measured using a spring scale On Earth, a baseball weighs 2.40 N On the moon, a baseball weighs 0.40 N

Physics 1D03 - Lecture 613 Mass is a measure of inertia : on the earth or on the moon, a 24.5 N force applied to the baseball will give it an acceleration of 100 m/s 2 (its mass is m = F/a = kg) We can compare masses with a balance, because of the remarkable property : Weights are equal when masses are equal

Physics 1D03 - Lecture 614 Newton’s Third Law (action and reaction) If object A exerts a force on object B, object B exerts an equal, opposite force back on A.

Physics 1D03 - Lecture 615 Newton’s Third Law : examples What is the “reaction” to the following forces? Block pushes down on table Gravity (of block) pulls earth up Balloon pushes on air outside You push on a block

Physics 1D03 - Lecture 616 A 140-kg wrestler and a 90-kg wrestler try to push each other backwards out of the ring. At first they are motionless as they push; then the large wrestler moves the other one backwards. Compare the forces they exert on each other. Which statement is correct? a)The forces are always equal. b)The larger wrestler always exerts a larger force. c)When they are motionless, the forces are equal; they start to move when the large wrestler exerts a larger force on his opponent than his opponent exerts back on him. Quiz

Physics 1D03 - Lecture 617 Contact Forces Examples : A heavy block on a table The table must push up on the block to prevent it from falling The type of contact force is called a normal force if it is perpendicular (normal) to the surfaces in contact. The normal force will be as large as necessary to hold the block (until the table breaks) Forces on Block

Physics 1D03 - Lecture 618 This is really an elastic force; the table behaves like a spring. At the atomic level, all contact forces are due to electromagnetic forces. If we look closely, the normal force arises from the table being bent : as the table tries to straighten, it pushes back.

Physics 1D03 - Lecture normal force : is perpendicular to the surfaces in contact - friction : is parallel to the surface friction has a more complex behaviour than the normal force (next lecture) We divide the contact force into two “components”