By the end of this unit, successful students will be able to:
- · Understand uniform circular motion of a particle so they can
- o Relate the radius of the circle or circumference of a circle and the speed or rate of revolution of the particle to the magnitude of centripetal acceleration. (AP Phys IE1a)
- o Describe the direction of the particle’s velocity and acceleration at any instant during the motion. (AP Phys IE1b)
- o Determine the components of the velocity and acceleration vectors at any instant, and sketch or identify graphs of these quantities. (AP Phys IE1c)
- o Analyze situations in which an object moves with specified acceleration under the influence of one or more forces so they can determine the magnitude and direction of the net force, or one of the forces that makes up the net force, in situations such as the following:
- § Motion in a horizontal circle (e.g. mass on a rotating merry-go-round, or car rounding a banked curve) (AP Phys IE1d1)
- § Motion in a vertical circle (e.g. mass swinging on the end of a string, cart rolling down a curved track, rider on a Ferris wheel). (AP Phys IE1d2)
- o Relate central forces to centripetal acceleration and solve problems using those relationships.
- · Understand that a field associates a value of some physical quantity with every point in space. Field models are useful for describing interactions that occur at a distance (long-range forces) as well as a variety of other physical phenomena
- o A vector field gives, as a function of position (and perhaps time), the value of a physical quantity that is described by a vector. (APPhys 2.A.1)
- · Understand conceptually Newton’s law of universal gravitation (1.11 Physics)
- · Use mathematical or computational representations to predict the motion of orbiting objects in the solar system. (NGSS HS-ESS1-4)
- · Use mathematical representations of Newton’s Law of Gravitation to describe and predict the gravitational forces between objects (NGSS HS-PS2-4)
- · The gravitational field caused by a spherically symmetric object with mass is radial and, outside the object, varies as the inverse square of the radial distance from the center of that object.(AP1 2.B.2)
- o The gravitational field caused by a spherically symmetric object is a vector whose magnitude outside the object is equal to C
- o Only spherically symmetric objects will be considered as sources of the gravitational field G (M/r^2)
- o (AP1 2.B.2.1) apply g = G (M/r^2) to calculate the gravitational field due to an object with mass M, where the field is a vector directed toward the center of the object of mass M.
- o (AP1 2.B.2.2) approximate a numerical value of the gravitational field (g) near the surface of an object from its radius and mass relative to those of the Earth or other reference objects.
- · Gravitational force describes the interaction of one object that has mass with another object that has mass. (AP1 3.C.1)
- o The gravitational force is always attractive
- o The magnitude of force between two spherically symmetric objects of mass m1 and m2 is G (m1*m2)/(r^2) where r is the center-to-center distance between the objects
- o In a narrow range of heights above the Earth’s surface, the local gravitational field, g, is approximately constant
- o Able to use Newton’s law of gravitation to calculate the gravitational force the two objects exert on each other and use that force in contexts other than orbital motion (AP1 3.C.1.1)
- o Able to use Newton’s law of gravitation to calculate the gravitational force between two objects and use that force in contexts involving circular orbital motion (AP1 3.C.1.2)
- · Explain Kepler’s Laws of Motion and use third law to solve problems. (AP Phys IF5b1)
- · Understand conceptually the concept of angular momentum and
- o that Kepler’s second law is a consequence of conservation of angular momentum
- o the relationship between torque and angular momentum
- Interpret Kepler’s third Law of Motion in terms of centripetal acceleration and Newton’s law of universal gravitation and use this interpretation to solve problems. (AP Phys IF5a1, AP Phys IF5a2)
All assignments are due on the date listed. That is not the date they are assigned.
Due date Day Assignment
11/21 Fri Read: Giancolli 5.1 – 5.5
Do: Questions pp. 129- 130: 1-10
11/26 Wed Half-Day
12/1 Mon Do: Giancolli Ch 5: 1, 6, 9, 12, 18, 19, 20, 25, 50, 68, 69
12/2 Tue Read: 5.6 – 5.9
Do: Questions: 11-18, 20-24
12/3 Wed Complete Centripetal Acceleration Lab
12/8 Mon Do: Giancolli Ch5: 33, 38, 40, 48, 57, 61, 62, 65, 67, 75, 83
12/9 Tue Test: Giancolli Chapter 5
12/10 Guest speaker?
12/16 Tue Complete Pendulum Lab
12/17 Wed Quest – Simple Harmonic Oscillators
12/18 Thu Project Presentations
12/23 Tue Project Presentations
12/23 Tue Project Papers due
Links - Circular Motion, Gravity, and Orbits
- Glencoe's support page for Chapter 7
- Glencoe's support page for Chapter 8
- Our text for AP Physics B has support for this material at Pearson Prentice Hall's page for Giancoli's Physics Chapter 5: Circular Motion; Gravitation
- Our text for AP Physics B has support for this material at Pearson Prentice Hall's page for Giancoli's Physics Chapter 8: Rotational Motion
- Haliday, Resnick and Walker's page on Chapter 11 - Rotation (Calculus based)
- Haliday, Resnick and Walker's page on Chapter 14 - Gravitation (Calculus based)
- Suggesting that there might be a law of conservation of great physicists, Isaac Newton was born in the year Galileo died. Newton (1642-1713) assembled the basis of much of classical mechanics in his Mathematical Principles of Natural Philosophy (1687) other copies can be found here and here and here wherein he decribes the relationships between forces, mass and acceleration as well as describes the nature of the force of univeral gravitation. All of these are English translations of the original Latin Principia. Newton was notorious for developing his briliant ideas about mathematics and physics and then not publishing them until much later. Many of the concepts embeded in the Principia were developed by Newton while away from Cambridge during the plague years of 1665-1666. His reticence to publish earlier helped lead to a number of conflicts concerning priority between Newton and his contemporaries such as Leibnitz, Hooke, and Huygens.
- Eric Ludlum maintains Siege Engine.com - a site centered around a Massachusetts group which designs and opperates catapults, trebuchets, and the like. Perfect for projectile motion, torque, potential energy and other mechanics problems.
- One nifty area of the Exploratorium site mentioned above is this section on Skateboard Science
- A number of specifications of the power, angular velocities, and torques of automobile, airplane, and boat motors can be found online. One such place is Marine Turbine Technologies' Turbine Outboard Propulsionpage.
- J-Track 3D Satellite Tracking Java program that shows you the orbits of satellites on this NASA site.
- MIT 8.01 Video 5: Uniform Circular Motion
- The Mechanical Universe 9: Moving in Circles
- MIT 8.01 Video 11: Work, Energy, and Universal Gravitation
- The Mechanical Universe 8: The Apple and the Moon
- Hula Cam. Switch to a rotating reference frame and watch hula-hooping from the point of view of the hoop.
- Bad Astronomy: Funhouse Galaxy. General Relativity describes how mass bends space through gravity -- one effect is the gravitational lensing of galaxies. Blog post by Phil Plait of Bad Astronomy w/ Hubble Telescope Pics.
- The Mechanical Universe 21: Kepler's 3 Laws
- The Mechanical Universe 22: The Kepler Problem
- The Mechanical Universe 24: Navigating in Space
- The Mechanical Universe 25: Kepler to Einstein
- The Mechanical Universe 25: Harmony of the Spheres
- MIT 8.01 Video 14: Orbits and Escape Velocity