Upload
others
View
2
Download
0
Embed Size (px)
Citation preview
β’ Semester preview
β’ Motion along a straight line
β’ Position and displacement
β’ Velocity and speed
β’ Acceleration as derivative of velocity with respect to time
β’ Interpret the sign of velocity and acceleration
Lecture 1: Course introduction
Motion in one dimension
Why study physics?
β’ Required for major
β’ Find out how the world works
β’ Because it is FUN
Demonstrations
Topic overview
Honda cog ad video
Mechanics
β’ Motion of macroscopic objects
β’ Forces, friction, circular motion
β’ Energy and momentum
β’ Motion of planets
β’ Rotational motion
β’ Oscillations and waves
β’ Fluids
Thermodynamics
A few tools:
β’ SI system of units, unit conversions
β’ Scientific notation
β’ Prefixes: micro, milli, centi, kiloβ¦
β’ Estimates
Please review on your own as needed.
See Ch. 1, Sec. 1.1-1.6
Basic math skills* required in this course
β’ Linear equations, systems of linear equations
β’ Quadratic equations
β’ Basic trigonometry: SOHCAHTOA, Pythagoras
β’ Calculus 1: derivatives/integrals
Note: Calc 1 is a prerequisite for this course. If you
have not taken calc 1, you must talk to your
recitation instructor ! *Special Homework # 1
will help you review
β’ Vectors (will be covered in lecture 3)
Kinematics: Describing Motion
Consider object as point mass β only translation
Things to know about a moving object:
Where is it? β Position
How fast is it moving and in which direction?
β Velocity
How do speed and direction of motion change?
β Acceleration
Position
β’ In reference to some coordinate system
β’ numerical value x
β’ x(t) is location of particle as a function of time
β’ Initial position: x0 = x(t0) *
* Does not mean x0 = 0
Showing position
With respect to a coordinate system:
x-axis with origin and a positive direction (arrow)
Mark position at certain times:
Displacement
Displacement = Change in position: *
Ξπ₯ can be positive or negative βΆ direction
Displacement is not the same as distance traveled!
Ξπ₯ = π₯π β π₯π
* Change (upper case delta Ξ) is the final
value of a quantity minus the initial value.
βI am currently going at 25 mphβ
= instantaneous speed
Speed and velocity
Together with information about
direction:
βI am currently going at 25 mph
North on Pine Streetβ
= instantaneous velocity
βI drove the 60 miles in one hourβ
= average speed, distance per time
Average velocity
ππ£πππππ π£ππππππ‘π¦ = π£π₯ =πππ πππππππππ‘
π‘πππ πππ‘πππ£ππ=βπ₯
βπ‘
π£π₯ > 0 : object moves in the positive x-direction
π£π₯ < 0 : object moves in the negative x-direction
* The subscript π₯ is
very important!unit: π
π
Average velocity and x-t graph
Average velocity
between t1 and t3:
π£π₯ = π£ππ£βπ₯ =π₯3 β π₯1π‘3 β π‘1
In this example:
π£π₯ is negative.
Object moves to
smaller value of x.
Speedometer shows
absolute value
of instantaneous velocity
π£ = |π£π₯| = speed
always positive
π£π₯ =ππ₯
ππ‘
Direction of velocity
π£π₯ >0: object moves in the positive x-direction
π£π₯ <0: object moves in the negative x-direction
Acceleration
ππ₯ =ππ£π₯ππ‘
=π2π₯
ππ‘2
Acceleration: how fast velocity changes,
time rate of change of velocity
Slope of π£π₯vs π‘ graph
Unit: ππ
π =
π
π 2
Acceleration produces change in velocity: ππ£π₯ = ππ₯ππ‘
Signs of acceleration and velocity
If π π₯ > 0 and thus ππ£π₯ = π π₯ππ‘ > 0:
if π£π₯ >0 speed up if π£π₯ <0 slow down
Signs of acceleration and velocity
if π£π₯ >0: slow down if π£π₯ <0: speed up
If π π₯ < 0 and thus ππ£π₯ = π π₯ππ‘ < 0:
Motion diagrams
http://phet.colorado.edu/en/simulation/moving-man
π₯0 = 0, π£0π₯ = +4π
π , ππ₯ = β2 π/π 2