The angular momentum vector for a spinning wheel lies along its axle and is pointed north. To make this vector point east with chagin magnitude it is necessary to exert a force of constant magnitude on the north end of the axle in which direction?

Options

A. always up
B. always down
C. at the initial moment in the east direction, but the force always remain perpendicular to the axle
D. always in the east direction

Explanation

To solve the problem, we need to understand how to change the direction of the angular momentum vector of the spinning wheel from pointing north to pointing east. We will use the right-hand rule to determine the direction of the torque required to achieve this change.

### Step-by-Step Solution:

1. **Identify the Initial Angular Momentum Direction**:
The angular momentum vector \( \vec{L} \) of the spinning wheel is initially directed north.

2. **Determine the Desired Angular Momentum Direction**:
We want to change the direction of \( \vec{L} \) so that it points east.

3. **Understand the Relationship Between Torque and Angular Momentum**:
The torque \( \vec{\tau} \) is related to the change in angular momentum by the equation:
\[ \vec{\tau} = \frac{d\vec{L}}{dt} \]
This means that a torque must be applied to change the angular momentum vector.

4. **Apply the Right-Hand Rule**:
To find the direction of the torque, we can use the right-hand rule. Point your thumb in the direction of the initial angular momentum (north) and then curl your fingers in the direction of the desired change (from north to east).

5. **Visualize the Rotation**:
As you rotate your wrist from north to east, your fingers will curl upwards. This indicates that the torque must be directed upwards.

6. **Conclusion**:
Therefore, to change the angular momentum vector from pointing north to pointing east, a force must be applied at the north end of the axle in the upward direction.

### Final Answer:
The direction of the force exerted on the north end of the axle must be **upward**.

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