Question

Angular momentum of a particle will not be zero, if the

• A. angle between position vector and linear momentum is 0°
• B. particle is at the origin
• C. angle between position vector and linear momentum is 90°
• D. linear momentum vanishes
• E. angle between position vector and linear momentum is 180°

Hint:

The angular momentum of a particle is zero when the position and momentum vectors are either parallel or antiparallel (0° or 180°), and non-zero when the angle is 90°.

Answer 1

The Correct Option is C

The angular momentum \( L \) of a particle is given by: \[ L = r \times p \] Where: - \( r \) is the position vector - \( p \) is the linear momentum vector Angular momentum will be zero when the position vector and the linear momentum vector are parallel or antiparallel (i.e., when the angle between them is either 0° or 180°), because the cross product of parallel or antiparallel vectors is zero. However, angular momentum will be non-zero when the angle between the position vector and linear momentum vector is 90° because the cross product will give a maximum value. Thus, the correct answer is (C) angle between position vector and linear momentum is 90°.