Physics #4 2/14/06 The Universal Gravitational Constant (G) Isaac Newton's Law of Universal Gravitation states that any two objects attract each other with a force equal to the product of their masses divided by the square of their separation times a
Rotation of a Rigid Body
Models for Objects:
A particle model: replaces a real object by a particle that has the
same mass as the actual object, but no shape or size. Can be used
the size or shape of the object do not affect its motion (e
Oscillatory motion: a repetitive (periodic) motion back and forth
about an equilibrium position.
Simple harmonic motion (SHM): sinusoidal oscillatory motion.
period of oscillation (T ): time to com
Forms of Energy
Energy of a system of particles:
kinetic (due to the motion of the particles);
potential (due to the interactions between the particles within the
system or with the environment).
Mechanical energy (Emech): kinetic + pote
In many situations, energy can be considered as
the ability to do work (make a change).
Energy can exist in different forms (kinetic,
gravitational potential, chemical, thermal, etc.).
Kinetic energy is the energy associat
Impulse and Momentum
Types of Interaction
Static interactions: forces exerted by two objects on each other
remain the same (e.g. equilibrium problems, projectile motion).
Dynamic interactions: forces exerted by two objects on each
other change d
Motion in a Plane
Dynamics in 2D
To find the components of an objects acceleration, one can use
the Newtons Second Law of Motion:
( Fnet ) x ( Fi ) x m x
( Fnet ) y ( Fi ) y m y
a x ( Fnet ) x / m
a y ( Fnet ) y / m
Once the components o
Motion in two and three
Kinematics in Two Dimensions
objects acceleration is parallel to its velocity at all times;
magnitude of the objects velocity (speed) may change;
direction of the objects velocity remains along the s
Newtons Third Law
Single-particle dynamics: the motion of a single object caused
by some external forces exerted on the object from the
An interaction: mutual influence of two systems on each other.
A force expre
Kinematics in 1D
Kinematics: part of mechanics that describes
motion itself (position, velocity, and
acceleration of an object at different times)
regardless of the causes of motion.
Dynamics: part of mechanics that analyzes the
Force and Motion
science of motion, that includes both kinematics and
dynamics, and studies the motion of physical objects,
as well as the forces that cause or limit those motions.
Force: definition (from d
Motion Along a Line
An object is in mechanical equilibrium when it has
Condition: net force acting on the object is zero.
Fnet Fi m a 0
( Fnet ) x ( Fi ) x m a x 0
( Fnet ) y ( Fi ) y m a y 0
Vectors & Coordinate
Scalars and Vectors
A scalar is a simple physical quantity that does not
depend on direction, and therefore does not depend
on the choice of a coordinate system.
Scalars can be described with a single number (size,
Concept of Motion
To study motion, we should define:
What is motion
Whats moving (the object)
Where the motion occurs (the
How do we describe
motion of an object
causes of motion
What is motion?
Motion means a change in the positi
Physics Sound Wave Speed March 21, 2006
Sound Wave Speed
If the speed at which sound waves traveled depended on frequency how would that change the way we perceive the world? At this time the speed of a sound wave, created by a pressure disturbanc
The Wave Model
Motion of matter:
Particle (finite mass, localized at just one point at any given time)
Rigid body (collection of particles, fixed size and shape)
Fluid (collection of particles, takes a shape of a container)