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183_notes:examples:a_meter_stick_on_the_ice [2014/11/16 21:20] – created pwirving | 183_notes:examples:a_meter_stick_on_the_ice [2014/11/20 15:59] – pwirving | ||
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=== Facts === | === Facts === | ||
+ | Mass of meter stick 300g | ||
+ | Pull at end of meter stick at right angles to the stick: 6N | ||
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=== Lacking === | === Lacking === | ||
+ | Rate of change of the center-of-mass speed $v_{CM}$? | ||
+ | Rate of change of the angular speed $\omega$? | ||
=== Approximations & Assumptions === | === Approximations & Assumptions === | ||
+ | No friction due to ice | ||
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=== Representations === | === Representations === | ||
+ | System: Stick | ||
- | {{course_planning:projects: | + | Surroundings: Your hand (pulling); ice (negligible effect) |
+ | {{183_projects: | ||
+ | $\frac{d\vec{P}}{dt}$ = $\vec{F}_{net}$ | ||
+ | $\frac{d\vec{L}_{rot}}{dt}$ = $\vec{\tau}_{net, | ||
- | === Solution === | + | $\tau = r_{A}Fsin \theta$ |
- | Direction: At both locations, the direction of the translational angular momentum of the comet is in the -z direction (into the computer); determined by using the right-hand rule. | ||
- | At location 1: | ||
- | $\mid\vec{L}_{trans, | ||
- | $= 1.1$ x $10^{30}$ $kg \cdot m^2/s$ | + | === Solution === |
+ | |||
+ | From the momentum principle: | ||
+ | |||
+ | $d\vec{P}/dt = d(m\vec{v}_{CM})/ | ||
+ | |||
+ | $dv_{CM}/dt = (6N)/ | ||
- | $\vec{L}_{trans, | + | Angular Momentum Principle about center of mass: |
+ | $d\vec{L}_{rot}/ | ||
- | At location 2: | + | Component into screen (-z direction): |
- | $\mid\vec{L}_{trans, | + | $Id\omega/ |
- | $= 1.1$ x $10^{30}$ $kg \cdot m^2/s$ | + | $d\omega/ |
- | $\vec{L}_{trans, | + | In vector terms, |