Final answer:
The question is seeking the angular acceleration of a roller, given its weight and another force. Given the moment of inertia and torque, the angular acceleration is calculated using Newton's second law for rotation, yielding an angular acceleration of 6.67 rad/s².
Step-by-step explanation:
The question provided, if P = 32 lb, asking for the angular acceleration of the 54-lb roller, is incomplete without additional context or equations that relate the force P to the angular acceleration of the roller. However, using the given moment of inertia (I) and the torque (τ), angular acceleration (α) can be calculated using Newton's second law for rotation: τ = Iα. From the information provided:
I = (0.500)(50.0 kg)(1.50 m)² = 56.25 kg · m².
Now, after we substitute the known values, we find the angular acceleration to be:
τ = 375 N·m
I = 56.25 kg · m²
α = τ/I = 375 N·m / 56.25 kg · m² = 6.67 rad/s²