To find the angular momentum given to the engine, we can use the following steps:

1. Calculate the Torque ($\tau$) created by the force: $\tau = r \times F$ where:

   • $r = 0.300 \, \text{m}$ (distance from the pivot),
   • $F = 350 \, \text{N}$ (force exerted).

   Substituting the values: $\tau = 0.300 \, \text{m} \times 350 \, \text{N} = 105 \, \text{N} \cdot \text{m}$

2. Calculate the Angular Impulse, which is equal to the change in angular momentum: $\text{Angular Impulse} = \tau \times t$ where $t = 0.325 \, \text{s}$.

   Substituting the values: $\text{Angular Impulse} = 105 \, \text{N} \cdot \text{m} \times 0.325 \, \text{s} = 34.125 \, \text{kg} \cdot \text{m}^2/\text{s}$

Therefore, the angular momentum given to the engine is: $\boxed{34.125 \, \text{kg} \cdot \text{m}^2/\text{s}}$

Would you like further explanation on any of these steps or concepts?

Here are some related questions to deepen your understanding:

1. What is the relationship between torque and angular momentum?
2. How would the angular momentum change if the distance from the pivot was increased?
3. What would happen to the angular momentum if the force was applied for a longer time?
4. Can you explain the concept of angular impulse in more detail?
5. How does maximum torque affect the efficiency of starting the engine?

Tip: Remember, angular momentum is conserved in a closed system with no external torques. This concept is essential in rotational dynamics problems.