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Chapter 6: Q16P (page 285)

In the discussion of Figure 3.8, we found for the angular momentum, the formula L=mrx(蝇虫谤).Use (3.9) to expand this triple product. If ris perpendicular to 蝇, show that you obtain the elementary formula, angular momentum =mvr.

Short Answer

Expert verified

The angular momentum L=m蝇r2鈥�r蝇.r

L=mvr Is proved.

Step by step solution

01

Given condition

The given angular momentum is L=mrx蝇虫谤

02

Concept Used

The value of a triple vector product is a linear combination of the two vectors in the parenthesis; the coefficient of each vector is the dot product oaf the other two; the middle vector in the triple product always has the positive sign.

03

Determine the angular momentum

Using the identity of the triple vector product:

.A脳B脳C=BC.A鈥�CB.AL=mr脳蝇脳r=m蝇r.r鈥�mr蝇.rL=m蝇r2-r蝇.r

The angular momentum L=m蝇r2-r蝇.r.

04

Determine the equation

From r is perpendicular to 蝇, 蝇.r=0

L=m蝇r2鈫�v=蝇rL=mvr

Hence proved.

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Given

F1=-2yi+(z-2x)j+(y+z)kF2=yi+2xj:

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