Lecture 9: Exam Review 1
recorded by: Massachusetts Institute of Technology, MIT
published: Oct. 10, 2008, recorded: September 1999, views: 2905
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1. Scaling Arguments:
The cross-sectional area of femurs should scale with mass if mother nature were protecting the femurs of large animals from crushing. But that is not the case. The diameter of a femur scales with its length. That protects the femurs against buckling (sideways deformation).
2. Dot Products:
Two methods are reviewed for obtaining the scalar product, by decomposition and by projection.
3. Cross Products:
The magnitude of the cross product equals the product of the magnitude of the two vectors and the sine of the angle between them. The direction of the vector product is determined using the right-hand corkscrew rule.
4. 1D Kinematics:
A graphic example of the position x(t) is given, and the velocity and acceleration are derived at various points in time. The average velocity and average speed are calculated. A plot of velocity vs. time is constructed.
Trajectories lie in a plane; they therefore reduce to 2 dimensional problems. A detailed example is worked using the trajectory of the "zero gravity" experiments in the KC135 (see Lecture 7).
6. Uniform Circular Motion:
The parameters for uniform (constant speed) circular motion are reviewed, including the equations for angular velocity and centripetal acceleration. The numerical example worked out is NASA's centrifuge to test astronauts; the centripetal acceleration is about 10g!
7. Brain Teaser with a Yardstick:
Professor Lewin slides his fingers underneath a yardstick, towards the center. Something strange happens, the fingers seem to take turns moving, they alternate sliding and stopping. Can you explain this?
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