Circular motion and gravitation

5 hours

6.1 – Circular motion


Essential idea: A force applied perpendicular to a body’s displacement can result in its circular motion.
Nature of science: Observable universe: Observations and subsequent deductions led to the realization that the force must act radially inwards in all cases of circular motion.
Understandings:
• Period, frequency, angular displacement and angular velocity Concept
• Centripetal force Concept Failed vertical loop Worse failed vertical loop
• Centripetal acceleration Concept 2D motion - choose circular Ladybug revolution Zero G Flight
Applications and skills:
• Identifying the forces providing the centripetal forces such as tension, friction, gravitational, electrical, or magnetic
• Solving problems involving centripetal force, centripetal acceleration, period, frequency, angular displacement, linear speed and angular velocity
• Qualitatively and quantitatively describing examples of circular motion including cases of vertical and horizontal circular motion
Guidance:
• Banking will be considered qualitatively only
Data Booklet reference:
v = wr
a = v2 / r = 4p2r / T2
F = mv2 / r = mw2r
• The v represents the tangential velocity of an object in circular motion at a radius r having an angular speed of w. The a represents the centripetal acceleration of an object moving in a circle of radius r at a speed v. The T represents the period of motion, the time to make one revolution if the objects speed is constant (uniform circular motion).
International-mindedness:
• International collaboration is needed in establishing effective rocket launch sites to benefit space programs
Theory of knowledge:
• Foucault’s pendulum gives a simple observable proof of the rotation of the earth, which is largely unobservable. How can we have knowledge of things that are unobservable?
Utilization:
• Motion of charged particles in magnetic fields (see Physics sub-topic 5.4)
• Mass spectrometry (see Chemistry sub-topics 2.1 and 11.3)
• Playground and amusement park rides often use the principles of circular motion in their design
Aims:
Aim 6: experiments could include (but are not limited to): mass on a string; observation and quantification of loop-the-loop experiences; friction of a mass on a turntable
Aim 7: technology has allowed for more accurate and precise measurements of circular motion, including data loggers for force measurements and video analysis of objects moving in circular motion


6.2 – Newton’s law of gravitation


Essential idea: The Newtonian idea of gravitational force acting between two spherical bodies and the laws of mechanics create a model that can be used to calculate the motion of planets.
Nature of science: Laws: Newton’s law of gravitation and the laws of mechanics are the foundation for deterministic classical physics. These can be used to make predictions but do not explain why the observed phenomena exist.
Understandings:
• Newton’s law of gravitation Concept My solar system Gravity and orbits Gravity force lab
• Gravitational field strength Concept Satellite about planet animation Curvature of space demonstration Wringing out a washcloth in orbit Lunar lander game nowykurier gravity simulator Physical model of true proportions of solar system
Applications and skills:
• Describing the relationship between gravitational force and centripetal force
• Applying Newton’s law of gravitation to the motion of an object in circular orbit around a point mass
• Solving problems involving gravitational force, gravitational field strength, orbital speed and orbital period
• Determining the resultant gravitational field strength due to two bodies
Guidance:
• Newton’s law of gravitation should be extended to spherical masses of uniform density by assuming that their mass is concentrated at their centre
• Gravitational field strength at a point is the force per unit mass experienced by a small point mass at that point
• Calculations of the resultant gravitational field strength due to two bodies will be restricted to points along the straight line joining the bodies
Data Booklet reference:
F = GMm / r2
g = F / m
g = GM / r2
• The F represents the gravitational force between two masses M and m whose centers are separated by a distance r. The universal gravitational constant G = 6.67x10-11 N m2 kg-2. The g represents the gravitational field strength at a distance r from the center of a mass M. It is also the acceleration due to gravity at that point in space.
Theory of knowledge:
• The laws of mechanics along with the law of gravitation create the deterministic nature of classical physics. Are classical physics and modern physics compatible? Do other areas of knowledge also have a similar division between classical and modern in their historical development?
Utilization:
• The law of gravitation is essential in describing the motion of satellites, planets, moons and entire galaxies
• Comparison to Coulomb’s law (see Physics sub-topic 5.1)
Aims:
Aim 4: the theory of gravitation when combined and synthesized with the rest of the laws of mechanics allows detailed predictions about the future position and motion of planets



TOPIC 6 PROBLEM SET

This is the complete problem set for Topic 6 - the same one I hand out. If you lose yours, you can download this one to replace it.




TOPIC 6 FORMATIVE ASSESSMENTS

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.



TOPIC 6 PROJECTS

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.



EXTENSION NOTES FOR ENRICHMENT

Foucault's Pendulum is really much more complex than our sample problem shows. The hourly precession of the pendulum's plane depends on the latitude of its location. Check out this derivation, if you dare!