Question

The angular momentum vector for a spinning wheel lies along its axle and is pointed north. To make this vector point east without changing its magnitude, it is not necessary to exert force of constant magnitude on the north end of the axle in which direction?
A. Always up
B. Always down
C. At the initial moment in east direction, but the force always remains perpendicular to the axle.
D. Always in the east direction.

Answer 1

Angular momentum is the momentum produced during an angular motion or rotational motion. As in this question, the angular momentum vector for a spinning wheel lies along its axle and is pointed north, firstly we can calculate torque. For finding the direction of force remember to take the cross product of \overrightarrow r $$$$ \times \overrightarrow F in such a way that it will give east direction.

Complete Step by step answer: consider, initially spin is moving along in such a way that its angular momentum is pointed towards north (as shown in figure). Due to torque, it is rotating, let’s say it is rotated by $d\theta$. Now this angular momentum vector is moving towards east (as shown)

$\overrightarrow {dL}$ is moving along the east direction.
So, torque will also go along the east direction.
\overrightarrow r $$$$ \times \overrightarrow F will be the direction of torque.
Here the direction of $\overrightarrow r$is given which is along the north direction. We need to find the direction of force in such a way that the cross product of those two values will give east direction. It means $\overrightarrow F$ must be along an upwards direction. Because $\overrightarrow r$ is along the north direction and when we cross product with $\overrightarrow F$, their resultant must be along the east direction. So, their angular momentum will change along the east direction.
So, option (A) is correct.

Note: Here Torque is responsible for the change in direction of angular momentum vector. We can use the right hand rule to determine the direction of the torque which is acting in this particular problem. Additionally, force is exerted on the north end of the axle that is required to turn the angular momentum vector from north to east.