Final answer:
To find the angular velocity and the time-average force acting on a rod after an impulsive blow, the moment of inertia needs to be calculated first, followed by using the impulse-momentum relationship for both linear and rotational motion.
Step-by-step explanation:
The student's question pertains to the rotational dynamics and impulse of a homogeneous rod subject to an impulsive force. Specifically, the problem involves a 96.6 lb rod in a vertical position when a 6 lb-sec impulse is applied at one end. To determine the angular velocity of the rod after the impulse, we need to apply the principle of impulse and momentum for rotational motion. We would use the formula:
I \( \times \) \( \Delta \omega \) = J, where I is the moment of inertia of the rod, \( \Delta \omega \) is the change in angular velocity, and J is the impulse applied.
For part (b), concerning the time-average force exerted by the pin at A, we would use the equation:
F \( = \frac{J}{\Delta t} \), where F is the time-average force, J is the impulse, and \( \Delta t \) is the impact time interval.
The moment of inertia of the rod about one end can be calculated using the formula I = (1/3)ML^2, where M is the mass of the rod, and L its length. Once we have I, we can determine the angular velocity after the impulse by dividing the impulse by the moment of inertia. The time-average force can be calculated by dividing the impulse by the time interval of the impact.