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183_notes:examples:a_meter_stick_on_the_ice [2014/11/16 21:26] – pwirving | 183_notes:examples:a_meter_stick_on_the_ice [2014/11/20 15:56] – 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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Surroundings: | Surroundings: | ||
- | {{course_planning: | + | {{183_projects:mi3e_11-050.jpg?300}} |
- | $d\vec{P}/dt = d(m\vec{v}_{CM})/dt = \vec{F}_{net}$ | + | $\frac{d\vec{P}}{dt}$ = $\vec{F}_{net}$ |
+ | |||
+ | $\frac{d\vec{L}}_{rot}{dt}$ = $\vec{\tau}_{net,CM}$ | ||
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From the momentum principle: | From the momentum principle: | ||
- | d | + | $d\vec{P}/dt = d(m\vec{v}_{CM})/ |
+ | |||
+ | $dv_{CM}/dt = (6N)/ | ||
+ | |||
+ | Angular Momentum Principle about center of mass: | ||
+ | |||
+ | $d\vec{L}_{rot}/ | ||
+ | |||
+ | Component into screen (-z direction): | ||
+ | |||
+ | $Id\omega/ | ||
+ | |||
+ | $d\omega/dt = (3N \cdot m)/[(0.3 kg \cdot m^2)/12] = 120 radians/ | ||
+ | |||
+ | In vector terms, $d\vec{\omega}/ |