Final answer:
The acceleration of pin B relative to the slot, given an angular velocity of θ_1 (clockwise) and an angular acceleration of θ_2 (counterclockwise), is θ_2 - θ_1. This is due to the convention that counterclockwise is positive and clockwise is negative for angular measurements.
Step-by-step explanation:
To answer the question of what the acceleration of pin B relative to the slot is, given that bar, AB has an angular velocity of θ1 in the clockwise direction and an angular acceleration of θ2 in the counterclockwise direction, we apply the concept of angular acceleration. By convention, the counterclockwise direction is considered as the positive direction for angular measurements. Therefore, if a bar has an angular velocity in the clockwise direction, we can denote it as negative. Conversely, an angular acceleration in the counterclockwise direction is positive.
Considering this, an angular velocity θ1 (clockwise) will be negative, while angular acceleration θ2 (counterclockwise) will remain positive. The net acceleration would be the addition of the two, considering their signs. Hence, the correct answer is d) (θ2 - θ1), where you subtract the angular velocity from the angular acceleration because they are in opposite directions.