2Kinematics – 18% Chapters 2,3,4 Position vs. displacementSpeed vs. VelocityAccelerationKinematic Equations for constant accelerationVectors and Vector AdditionProjectile Motion – x,y motion are independentUniform Circular Motion
3Kinematics – Motion in One and Two Dimensions Key Ideas and VocabularyMotion in the x is independent from motion in the yDisplacement, velocity, accelerationGraphical Analysis of Motion –x vs. t - Slope is velocityv vs. t - Slope is acceleration- Area is displacementa vs. t – Can be used to find the change in velocityCentripetal Acceleration is always towards the center of the circle
4Kinematics – Motion in One and Two Dimensions Constant AccelerationMotion EquationsCentripetal Acceleration
5Newton’s Laws of Motion – 20% Chapters 5 & 6 Newton’s Three Laws of MotionInertiaFnet = maEqual and opposite forcesForceWeight vs. MassFree Body DiagramsTension, Weight, Normal ForceFriction – Static and Kinetic, Air ResistanceCentripetal Forces and Circular MotionDrag forces and terminal speed
6Newton’s Laws of Motion Second Law Problems Newton’s Second Law –Draw free body diagram identifying forces on a single objectBreak forces into componentsApply 2nd Law and solve x & y components simultaneouslyInclined Plane –Rotate axes so that acceleration is in the same direction as the x-axis
7Newton’s Laws of Motion Circular Motion Problems Draw free body diagram identifying forces on a single objectBreak forces into componentsApply 2nd Law and solve x & y components simultaneouslyRemember that the acceleration is centripetal and that it is caused by some force
8Newton’s Laws of Motion Air Resistance – Drag Force Identify forces and draw free body diagramsMay involve a differential equationExample:Separate variables and solve. Should end up with something that decreases exponentiallyTerminal Velocity – Drag force and gravity are equal in magnitude – Acceleration is equal to zero
9Work, Energy, Power – 14% Chapters 7 & 8 Kinetic EnergyWork – by constant force and variable forceSpring ForcePowerPotential Energy – gravitational, elasticMechanical EnergyConservation of EnergyWork Energy Theorem
10Work, Energy and Power Key Equations Work by a Constant ForcePowerKinetic EnergyWork-Energy Theorem
12Potential Energy Curves Slope of U curve is –FTotal energy will be given, the difference between total energy and potential energy will be kinetic energy
13Systems & Linear Momentum – 12% Chapters 9 & 10 Center of MassLinear MomentumConservation of MomentumInternal vs. External forcesCollisions – Inelastic, ElasticImpulse
14Systems & Linear Momentum Key Equations Center of MassMomentumConservation of MomentumImpulse
15Systems & Linear Momentum Center of Mass, Internal and External forces Center of Mass can be calculated by summing the individual pieces of a system or by integrating over the solid shape.If a force is internal to a system the total momentum of the system does not changeOnly external forces will cause acceleration or a change in momentum.Usually we can expand the system so that all forces are internal.
16Systems & Linear Momentum Collisions Inelastic collisions – (objects stick together)Kinetic energy is lostMomentum is conservedElastic Collisions – (objects bounce off)Kinetic energy is conserved
17Systems & Linear Momentum Impulse Impulse is the change in momentumMomentum will change when a force is applied to an object for a certain amount of timeArea of Force vs Time curve will be the change in momentum
18Systems & Linear Momentum Conservation of Momentum Momentum will always be conserved unless an outside force acts on an object.Newton’s Second Law could read:Newton’s Third Law is really a statement of conservation of momentumSet initial momentum equal to final momentum and solve – make sure to solve the x and y components independently
19Circular Motion and Rotation – 18% Chapters 11 & 12 Uniform Circular Motion (chap 4 & 6)Angular position, Ang. velocity, Ang. AccelerationKinematics for constant ang. AccelerationRelationship between linear and angular variablesRotational Kinetic EnergyRotational Inertia – Parallel Axis TheoremTorqueNewton’s Second Law in Angular form
20Circular Motion and Rotation – 18% Chapters 11 & 12 Rolling bodiesAngular momentumConservation of Angular momentum
21Circular Motion and Rotation Basic Rotational Equations Circular Love and Angular KinematicsAngular Velocity & Acceleration
22Circular Motion and Rotation Linear to Rotation As a general rule of thumb, to convert between a linear and rotational quantity, multiply by the radius r
23Circular Motion and Rotation Rolling and Kinetic Energy A rolling object has both translational and rotational kinetic energy.
24Circular Motion and Rotation Moment of Inertia How something rotates will depend on the mass and the distribution of massParallel Axis Theorem – allows us to calculate I for an object away from its center of massI for the Center of Massm – total massH – distance from com to axis of rotation
25Circular Motion and Rotation Moment of Inertia For objects made of multiple pieces, find the moment of inertia for each piece individually and then sum the moments to find the total moment of inertiaAxis of rotationm2m1L
26Circular Motion and Rotation Torque Rotational analog for force – depends on the force applied and the distance from the axis of rotationIf more than one torque is acting on an object then you simply sum the torques to find the net torqu
27Circular Motion and Rotation Angular Momentum Angular momentum will always be conserved in the same way that linear momentum is conservedAs you spin, if you decrease the radius (or I) then you should increase speed to keep angular momentum constant
28Circular Motion and Rotation Newton’s 2nd Law for Rotation
29Oscillations and Gravity – 18% Chapters 14 & 16 Frequency, Period, Angular FrequencySimple Harmonic MotionPeriod of a SpringPendulumsPeriodSimplePhysical
30Oscillations All harmonic motion will can modeled by a sine function The hallmark of simple harmonic motion isKnowing the acceleration you can find ω.
31Oscillations Springs and Simple Pendulums Ideal SpringSimple Pendulum
32Oscillations Physical Pendulum A physical pendulum is any pendulum that is not a string with a mass at the end. It could be a meter stick or a possum swinging by its tail.
33Oscillations and Gravity – 18% Chapters 14 & 16 Law of GravitationSuperposition – find force by adding the force from each individual objectShell Theorem – mass outside of shell doesn’t matterGravitational Potential EnergyOrbital Energy – Kinetic plus PotentialEscape SpeedKepler’s Laws’Elliptical OrbitsEqual area in equal time (Cons. of Ang. Momentum)T2 α R3 - can be found from orbital period and speed
34Gravity A very serious matter Universal Law of GravityGravitational Potential EnergyCircular Orbit Speed