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Lecture 3: Two- and Three-Dimensional Motion
August 29, 2017
Reading Assignment
- Read: 3-1, 3-2, 3-3, 3-6
- Study: Figs 3.1, 3.2, 3.4; Ex 3.1; Got It 3.2; Figs 3.7, 3.8, 3.9; Exs 3.2, 3.7, 3.8
Objectives
- (Continuing objective) Relate concepts of classical mechanics to “everyday” situations and discuss various applications of the concepts to practical problems in various fields of science, medicine and engineering.
- Describe vector quantities using: a) magnitude and direction, b) rectangular components, and c) unit vectors. Be able to convert from one description to another.
- Draw a sketch showing the addition of vectors. Calculate the vector sum quantitatively using the method of components.
- Given an object's path in space (in unit vector notation or a diagram) in two or three dimensions, determine its velocity and acceleration at various locations and times.
- Analyze uniform circular motion by relating period, velocity, radius, and acceleration, including the directional properties of velocity and acceleration.
Homework
- Wednesday's Assigned Problems:
A7, A8; CH 3: 4, 5, 15, 17, 23, 25, 28, 29, 43
Answers: CH 3 #28 $259\, \hat{\imath} + 65.9\, \hat{\jmath}\,\text{km/h}$
Notes: For CH 3 #15, delete the word “graphically”.
- Monday's Hand-In Problems:
A9, A10, A11, A13; CH 3: 18, 48, 54; CH 4: 30, 54,
58abcd
Notes: For CH 3 #48b, replace “average speed” with “magnitude of the average velocity.” For CH 4 #54, assume the two blocks have the same acceleration.
Lecture Materials
- Click here for the Lecture overheads
or here for full-sized versions.
Answers to ConcepTests: (1) 5; (2) look at the diagram that you drew (or the one from lecture) to answer these; (3) 2; (4) 3; (5) 3; (6) 2
Videos of example problems
For the first one, to see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.- Video Example #1: This is a worked out vector addition problem, good practice with adding vectors. ans: $1.15\, \mbox{m}$ at $84^\circ$ S of E
- A relative velocity example
- A harder relative velocity example, this one about a layson albatross (layson albatrosses are really cool). NOTE: there is an arithmetic error at the 7 min mark of this video. I have incorrectly subtracted the y-components. 6.0 - (-16.8) is 22.8, not 10.8, and that error propagates through the rest of the problem. Sorry.
Pre-Class Entertainment
- City of New Orleans, by Arlo Guthrie
- Cars, by Gary Numan
- Crazy, by Seal
- Come With Me Now, by Kongos
- Chocolate, by The 1975
- Change, by Churchill
Relative motion example of the day
Movie taken at the beach of a bird flying into the wind.Seagulls flying in windy conditions -- similar to my research on "active" (self-propelled) tracers in fluid flows. pic.twitter.com/RkQ5CYFDRp
— Tom Solomon (@TheChaoticBird) August 10, 2017