Lecture 29: Exam Review 3
recorded by: Massachusetts Institute of Technology, MIT
published: Oct. 10, 2008, recorded: November 1999, views: 14537
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1. Review of 1D Collisions:
Two masses moving in one dimension collide in a completely inelastic manner. The equations for an elastic collision are also discussed.
2. Atwood's Machine:
A "massless" rope runs (without slipping) over a pulley (the moment of inertia of the pulley is not negligible). The rope has a pair of masses hanging from it. The equations of rotational (pulley) and translational (the 2 masses) motion are related, and solved for the acceleration of the masses.
3. SHO of a Suspended Rod:
A pendulum consists of a ruler/rod suspended from one end. The equation of motion is derived. The moment of inertia is determined using the parallel axis theorem. Rotational kinetic energy is also discussed. For small angles, the motion is that of a simple harmonic oscillator.
4. Conservation Laws for a Satellite's Orbit:
A satellite is launched from a planet. Using the conservation of angular momentum and mechanical energy, and the maximum distance between the planet and satellite, one can calculate the launch velocity and other orbital parameters.
5. Doppler Shift Review:
If stars are receding from us, the starlight that we observe is red-shifted; the observed wavelengths are longer than those emitted by the star. The Doppler shift depends on the component of the velocity along the line-of-sight (so-called radial velocity). A somewhat similar equation applies to sound received from moving sound sources. However, in the case of sound, it DOES matter whether the sound source moves or whether the observer moves. For light, only the relative motion between source and observer matters.
6. Pure Roll:
The acceleration of a cylinder and sphere is derived under the condition of pure roll. A sliding object accelerates faster down an incline plane than a rolling object. The static friction coefficient must be sufficient to support pure roll. Kinetic energy for a rolling object has both a translational and rotational term.
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