Question

Figure 11-29 shows a particle moving at constant velocity and five points with their xycoordinates. Rank the points according to the magnitude of the angular momentum of the particle measured about them, greatest first.

Short answer

Rank of the points according to the magnitude of the angular momentum of the particle measured about them is,

.$L_b>L_c=L_d>L_a=L_e$

Step-by-step solution

Step 1: Given

Figure is given to rank the points according to the magnitude of the angular momentum of the particle measured about them.

Understanding the concept of angular momentum

Using the equation of angular momentum, rank the points according to the magnitude of the angular momentum of the particle measured about them.

The formula is as follows:

$\begin{array}{c}L=r\times P\\ =rP\sin \theta \end{array}$

Where,$\theta$ is the angle between $P$and the position vector$r.$

Step 3: Ranking the points according to the magnitude of the angular momentum of the particle measured about them

Now,

$\begin{array}{c}L=r\times P\\ =rP\sin \theta \end{array}$

For points a and e, the angle between the momentum vector and the distance from the moving particle to points a and e is zero. So,

From figure,$r=4$for point a andfor$r=8$point b,

$L_a=\left(4\right)\left(P\right)\sin 0=0$

$L_e=\left(8\right)\left(P\right)\sin 0=0$

For point c, the angle between the momentum vector and the position vector is${90}^0.$So,$r=\sqrt{13}$

From figure,$r=2$for point c,

$L_c=\left(2\right)\left(P\right)\sin {90}^0=2P$

For point b, the angle between the momentum vector and the position vector is ${108}^0.$So,

From figure $r=\sqrt{13}$, for point b,

$L_b=\sqrt{13}\left(P\right)\sin {108}^0=3.42P$

For point d, the angle between the momentum vector and the position vector isSo,

From figure,$r=\sqrt{13}$for point d,

$L_d=\sqrt{13}\left(P\right)\sin {33.69}^0=2P$

Therefore,

$L_b>L_c=L_d>L_a=L_e$

Hence, using the equation of angular momentum, the points can be ranked according to the magnitude of the angular momentum of the particle measured about them and the rank is,

.$L_b>L_c=L_d>L_a=L_e$