A single force acts on a particle P.Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.
A)1, 2, 3, 4
B)1 and 2 tie, then 3, then 4
C)1 and 2 tie, then 4, then 3
D)1 and 2 tie, then 3 and 4 tie
E)All are the same

Question

A single force acts on a particle P.Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest. 
A)1, 2, 3, 4 
B)1 and 2 tie, then 3, then 4 
C)1 and 2 tie, then 4, then 3 
D)1 and 2 tie, then 3 and 4 tie 
E)All are the same

Quizplus · Accepted Answer

The time rate of change of the particle's angular momentum about point O is given by the cross product of the position vector and the force. Thus, we need to compare the magnitudes of the cross products in each orientation. 
In orientation 1, the force is perpendicular to the position vector, so the cross product has a magnitude of Fd, where d is the distance from P to O. 
In orientation 2, the force is at an angle to the position vector, so the cross product has a magnitude of Fd sin(theta), which is less than Fd. 
In orientation 3, the force is parallel to the position vector, so the cross product is zero and there is no time rate of change of angular momentum. 
In orientation 4, the force is in the opposite direction to the position vector, so the cross product has a magnitude of -Fd, which is greater than Fd. 
Therefore, the order from least to greatest magnitude of time rate of change of angular momentum is 1 and 2 tie (both have magnitude Fd), followed by 4 (magnitude -Fd), and then 3 (magnitude 0). The correct choice is C.

A Single Force Acts on a Particle P