Kinematics Review Kinematics Review a) Exam information b) What kind of questions? c) Review

First Midterm Exam on Monday Covers Units 1-3 plus “Math” One-dimensional Kinematics Two-Dimensional Kinematics Relative and Circular Motion Unit conversion Trigonometry and Algebra 50 minute duration Multiple choice Calculators Allowed/Needed Three sheets of notes. (equivalent font size>9)(this is font size=9)

What type of questions? Interpretation and use of graphs Which of the following statements about the velocity of the cart is correct? What is the velocity at t=? What is the acceleration at t= ? ….

What type of questions? Displacement, velocity and acceleration in 1 dimension Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

What type of questions? Motion with constant acceleration in 1-dimension V0=0m/s ground H=10m V1 Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

What type of questions? Relative motion in 2 dimensions Given some combination of relative velocity between frames of reference answer questions related to the displacement and elapsed times for certain actions…

What type of questions? Projectile motion Given some combination of initial velocity, range , maximum height, etc…calculate characteristics of projectile motion.. Be prepared to re-arrange equations to obtain initial velocity, etc. from other parameters…

What type of questions? Circular Motion Top view Given some combination of angular velocity, Radius, ac calculate a characteristic of the motion of an object at constant speed in a circle…

What type of questions? Any material from Units 1-3 Calculations Unit conversion Algebra, trigonometry and vectors Conceptual Questions Similar to pre-lecture and checkpoint questions

What type of questions? Vectors q Decompose a vector into polar or Cartesian coordinates Vector Addition (Subtraction)

How to prepare? Read the textbook/Review the video prelectures Review the lecture slides (Re-)Work homework problems Look at last year’s exam and solutions http://www.physics.utah.edu/~springer/phys1500/exams/ Prepare three sheets of notes Basic Fundamental Equations Derived Equations( and be able to derive them!) Unit conversions Algebra notes (quadratic equation) Trigonometric relations Vector concepts Conceptual notes,… Get enough sleep!!!

Main Points of Unit 1

Main Points of Unit 1

Vectors and 2d-kinematics – Main Points

Vectors and 2d-kinematics – Main Points

Vectors and 2d-kinematics Important Equations

Relative and Circular Motion a) Relative motion b) Centripetal acceleration

Hyperphysics Motion Displacement vs timet Velocity vs timet Acceleration vs timet

Hyperphysics Motion

1d-Kinematic Equations for constant acceleration Basic Equations to be used for 1d – kinematic problems. Need to apply to each object separately sometimes with time offset When acceleration changes from one constant value to another say a=0 The problem needs to be broken down into segments

Maximum Height of ball thrown upward in gravitational field What is the velocity of an object when it is at its maximum height? Two ways to solve for maximum height… Solve for time first Solve for position directly Remember a is negative Use tf to solve for maximum height…

The meeting Problem Whenever possible solve symbolically. Define your problem; Identify useful equations Whenever possible solve symbolically. Then plug in the numbers!!!! You can understand what is going on better if you keep the equations organized. Start solving… Gather terms…Does the equation look reasonable? Solve for desired quantity… Position of object 1 when object 2 is launched This time is w.r.t object 2. To obtain time w.r.t object 1 need to add delay time Speed of object 1 when object 2 is launched

Break problem into parts Region 1: 0<t<1.5 s Region 1 Region 2 Region 3 Region 2: 1.5s<t<3.0s What happened in region 3? Region 3: 3.0s<t<5.0s Smartphysics Conclusion

2d-Vectors q Think of a vector as an arrow. (An object having both magnitude and direction) The object is the same no matter how we chose to describe it 25

Algebra and Trigonometry Algebra is “fair” Quadratic Equation Trigonometry

Vector Addition Add Components!!! AddTail to Head 27

Kinematics in 3D Note: 3 directions are independent, but share time. 28

Projectile Motion Horizontal Vertical Boring 29

Ballistic Projectile Motion Quantities Initial velocity speed,angle Maximum Height of trajectory, h=ymax “Hang Time” Time of Flight, tf Range of trajectory, D Height of trajectory at arbitrary x,t

Derived Projectile Trajectory Equations Maximum height Given some combination of initial velocity, range , maximum height, etc…calculate characteristics of projectile motion.. Be prepared to re-arrange equations to obtain initial velocity, etc. from other parameters… Time of Flight (“Hang Time”) Range of trajectory Height of trajectory as f(t) , y(t) Height of trajectory as f(x), y(x)

Launch Velocity-Given R and 

Launch Angle

Launch Velocity –Given R and h

Relative Motion in 2 Dimensions Speed relative to shore

Relative Motion in 2 Dimensions Direction w.r.t shoreline

Centripetal Acceleration Constant speed in circular path Acceleration directed toward center of circle What is the magnitude of acceleration? Proportional to: Speed time rate of change of angle or angular velocity v = wR

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013

Midterm 1 2013