Question

If the velocity is 7 = 3i+2j+ 4k and the position vector is i=-i+3j-2k for a body of mass M, the angular momentum L
is?

Answer 1

Answer:

L= M(16i-10j-7k)

Explanation:

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Answer 2

Answer:

Angular Momentum of the body is   L = m(16i-2j-11k)

Explanation:

Angular momentum of the body is the momentum when body moves a circular motion. It is denoted by L and is expressed as following relation

  L = r × p

    where p = linear momentum

                r = postion of  object

Given : r= -i+3j-2k

            v= 3i+2j+4k

Now Angular momentum is

   L= r × p

   L =r × mv

  L= m(r × v)   -----(i)

to calculate (r × v) =

$\left[\begin{array}{ccc}i&j&k\\-1&3&-2\\3&2&4\end{array}\right] \\\\=i(12+4)-j(-4+6)+k(-2-9)\\\\=16i -2j -11k$

So , putting this in (i)    

   L = m(16i-2j-11k)

Hence this is required angular momentum vector

 Magnitude of angular momemtum is

$m\sqrt{16^{2}+(-2)^{2} +(-11)^{2} } \\\\m\sqrt{256+ 4+ 121} \\\\m\sqrt{381}\\ \\=19.51m$

Hence Magnitude of angular momentum vector is 19.51m