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Example: A Meter Stick on the Ice
Consider a meter stick whose mass is 300 grams and that lies on ice (see representation in which we are looking down on the meter stick). You pull at one end of the meter stick, at right angles to the stick, with a force of 6 newtons. Assume that friction with the ice negligible. What is the rate of change of the center-of-mass speed $v_{CM}$? What is the rate of change of the angular speed $\omega$?
Facts
Lacking
Approximations & Assumptions
Representations
Solution
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:
$\mid\vec{L}_{trans,Sun}\mid$ = $(8.77$ x $10^{10}m)(2.2$ x $10^{14}kg)(5.46$ x $10^4m/s)sin 90^{\circ}$
$= 1.1$ x $10^{30}$ $kg \cdot m^2/s$
$\vec{L}_{trans,Sun}$ = $\langle{0, 0, -1.1 x 10^30}\rangle$ $kg \cdot m^2/s$
At location 2:
$\mid\vec{L}_{trans,Sun}\mid$ = $(1.19$ x $10^{12}m)(2.2$ x $10^{14}kg)(1.32$ x $10^4m/s)sin 17.81^{\circ}$
$= 1.1$ x $10^{30}$ $kg \cdot m^2/s$
$\vec{L}_{trans,Sun}$ = $\langle{0, 0, -1.1 x 10^30}\rangle$ $kg \cdot m^2/s$