The position vector r and the velocity vector v of the object are given as:
\(-\vec r = 3 \hat i - \hat j m\)
\(- \vec v = 3 \hat j + \hat k m/s\)
The mass m of the object is 1 kg.
The linear momentum \(\vec p\) is given by the formula:
\(\vec p = m\vec v\)
Substituting the values:
\(\vec p = 1.(3\hat j + \hat k) = 3 \hat j + \hat k\, kg\, m/s\)
The angular momentum \(\vec L\) is given by the cross product of the position vector \(\vec r\) and the linear momentum \(\vec p\):
\(\vec L= \vec r \times \vec p\)
Substituting the values:
\(\vec L = (3\hat i - \hat j) \times (3 \hat j + \hat k)\)
We can calculate the cross product using the determinant:
Calculating the determinant, we expand it as follows:
Calculating each of these determinants:
The magnitude of \(\vec L\) is given by:
We are told that the magnitude of angular momentum is √x Nm. Therefore, we have:
√x = √91
This implies:
x = 9
