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

Midterm 3 Exam in-class Average = 5.1/12 Average = 57% (normalized to 9) The score for Midterm 3 will be calculated with the following formula:

Final Exam Review the following material homework problems. video pre-lectures/textbook. Lecture slides Unit Main Points Multiple choice…but show your work and justification. Mostly Calculations…”step by step” Some Conceptual questions…like checkpoint problems. Bring calculators and up to ten sheets of notes. It is best to prepare your own hand-written notes! Derived Equations may be helpful…(e.g. projectile motion)

Kinematics Force Energy Conservation Laws Collisions Rotations What we covered… Kinematics Description of Motion Force Dynamics-how objects change velocity Energy Kinetic and Potential Conservation Laws Momentum and Energy Collisions Elastic and In-elastic Rotations Torque/ Angular Momentum/Statics

Problem Solving Techniques Visualize/Diagram “Sketch” problem Identify variables, input and what we are trying to solve Free-body diagrams Express in Mathematical Equations Scalars-1d Vectors-2d,3d Break into components System of n-equations with n-unknowns Use Mathematical tools to solve: Quadratic Equation Vector operations Trigonometry Conceptual Understanding Does answer make sense?

Potential Problem Topics Projectile Motion Relative Motion - 2d Uniform Circular Motion Forces Weight (near earth) Gravitational (satellite) Springs Normal Force Tension Friction Free-Body Diagrams Work-Kinetic Energy Potential Energy Center of Mass Conservation of Momentum Collisions In-elastic Elastic Rotations Kinematics Dynamics Statics Moment of Inertia Torque Angular Momentum

Relevant Formulae

Relevant Formulae

Kinematics

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

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 Time of Flight (“Hang Time”) Range of trajectory Height of trajectory as f(t) , y(t) Height of trajectory as f(x), y(x)

Relative Motion in 2 Dimensions Direction w.r.t shoreline Speed relative to shore

Uniform Circular Motion

Uniform Circular Motion 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

Dynamics

Inventory of Forces Weight Normal Force Tension Gravitational Springs …Friction

http://hyperphysics.phy-astr.gsu.edu/hbase/N2st.html#c1

m2 1) FBD N T m2 g f T m1 m1 m2g m1g 22

m2 N T m2 f T m1 m2g N = m2g m1g m1g – T = m1a T – m m2g = m2a 1) FBD 2) SF=ma N T m2 g f T m1 m1 m2g N = m2g m1g T – m m2g = m2a m1g – T = m1a add m1g – m m2g = m1a + m2a m1g – m m2g a = m1 + m2 23

m2 N T m2 f T m1 m2g m1g m1g – T = m1a T = m1g – m1a 1) FBD 2) SF=ma g m1g – m m2g T = m1g – m1a a = m1 + m2 T is smaller when a is bigger 24

Gravitation Problems…too!

Be careful what value you use for r Be careful what value you use for r !!! Should be distance between centers of mass of the two objects

Work-Kinetic Energy Theorem The work done by force F as it acts on an object that moves between positions r1 and r2 is equal to the change in the object’s kinetic energy: But again…!!!

Energy Conservation Problems in general For systems with only conservative forces acting Emechanical is a constant

(otherwise objects velocity is constant) Determining Motion Force Unbalanced Forces  acceleration (otherwise objects velocity is constant) Determine Net Force acting on object Use kinematic equations to determine resulting motion Energy Total Energy  Motion, Location Work Conservative forces Motion from Energy conservation

Friction “It is what it has to be.”

Block

Work & Kinetic Energy

Example Problem

Potential Energy

Example Problems

Example: Pendulum h h Conserve Energy from initial to final position.

Gravitational Potential Problems conservation of mechanical energy can be used to “easily” solve problems. Define coordinates: where is U=0? Add potential energy from each source. as

Collisions Center of Mass Conservation of Momentum Inelastic collisions Elastic Collisions Impulse and Reference Frames Multiple particles, Solid Objects Isolated system, No external force Non-conservative internal force Conservative internal force Individual Particle changes momentum due to Force acting over a given duration Favg = DP/Dt

Systems of Particles

Example Problem

Collisions

Example Problem

Example Problem :

Impulse

|Favg | = |DP | /Dt = 2mv cosq /Dt

Rotations Rotational Kinematics Moment of Inertia Torque Rotational Dynamics Rotational Statics Angular Momentum Description of motion about a center of mass Resistance to changes in angular velocity Force applied at a lever arm resulting in angular acceleration Newton’s 2nd law for rotations How to ensure stability Vector Quantity describing object(s) rotation about an axis

Rotational Kinematics

Rotational Dynamics

Example Problem

Example Problem

Work & Energy (rotations)

Example Problem

Statics

Statics Problems

Example Problem

Angular Momentum

Example Problem

Relevant Formulae

Relevant Formulae